Short Answer
What is legally required to partition a U.S. State?
Under the U.S. Constitution, a partition of a state must be approved by Congress in a simple law, and by any state whose territory is impacted by the partition. That's it.
Article IV, Section 3, Clause 1 of the U.S. Constitution is controlling and it says:
New states may be admitted by the Congress into this union; but no new
states shall be formed or erected within the jurisdiction of any other
state; nor any state be formed by the junction of two or more states,
or parts of states, without the consent of the legislatures of the
states concerned as well as of the Congress.
In other constitutional contexts, the term "consent of the legislature" has been interpreted to mean "by state law" or "by a state constitution approved process" (e.g. redistricting by a state constitution approved commission following a census has been upheld), rather than literally. But the case law interpreting that phrase as it appears in the U.S. Constitution in different places and contexts has not been entirely consistent.
Certainly, a bill passed by the state legislature of a state for which a partition was proposed, which was also signed by the Governor of the state and enacted into law, even if the Governor's signature was determined to not be constitutionally required, would suffice to comply with Article IV, Section 3, Clause 1 of the U.S. Constitution.
Are there precedents for this?
Yes. There are several precedents for this discussed below in the next section of this answer. Kentucky and Maine are the cleanest examples.
Could Republicans do anything to delay or stop the partition of a U.S. State if Democrats controlled both houses of Congress and the Presidency?
Assuming Democrats control the presidency, Senate, and House in 2021,
what can Republican legislators do to stop such an action?
Not really.
A bill to admit a new U.S. state is currently subject to filibuster in the U.S. Senate, which would require a 60% majority to bring the matter to a vote, which the Democrats are unlikely to have in the U.S. Senate. But prior precedents in the U.S. Senate under both Democratic and Republican control of the U.S. Senate in the last decade recognize the "nuclear option" which would allow the U.S. Senate to abolish the filibuster for this type of bill by majority vote (i.e. 51 votes, possibly including the vice president's tie breaking vote). Democrats used the nuclear option in November of 2013, to force votes on President Obama's nominees to offices other than the U.S. Supreme Court. Republicans expanded the nuclear option in April of 2017 to include U.S. Supreme Court nominations. The legislative filibuster remains in the U.S. Senate rules but could be abolished at any time by majority vote under these widely accepted precedents.
So, while a Republican minority in the U.S. Senate could force a change in the U.S. Senate rules to delay the admission of a new U.S. state or the partition of an existing U.S. state, this would basically be a "road bump."
A Republican minority in the U.S. House would have no formal power to limit such a bill, but could propose floor amendments to the bill allowed by the U.S. House Rules Committee.
Historical Background For This And Related Matters
The history of state formation, sometimes from the territory of other U.S. states in the U.S. is obscure, but interesting.
Historical Precedents
This has been done multiple times in the past.
Vermont (1791 in the face of a claim to its territory from New York of disputed validity, arguably it was more analogous to the annexation of Texas which was an independent country before becoming a U.S. state), Kentucky (1792 from Virginia), Maine (1820 from Massachusetts), and West Virginia (1863 from Virginia, but see below and without the consent of the Virginia legislature due to the U.S. Civil War) were all made from territory claimed by another state.
For context, the American Revolution was commenced in 1776, but the colonies were governed under the Articles of Confederation until the current U.S. Constitution was adopted in 1789 (two years after the adoption of the Northwest Ordinance under the Articles of Confederation which were foundational in the organization of most of the U.S. states in the Midwest). The Bill of Rights was adopted in 1791. The U.S. Civil War was from 1861 to 1865.
All four of these cases involve predominantly rural, thinly populated territory and took place a long time ago. The most recent took place 157 years ago.
The process used in the case of Kentucky is something of the model for how Article IV, Section 3, Clause 1 was intended to work and also benefitted from the fact that it took place just three years after that provision was adopted with almost all of its drafters still active in American politics at the time:
The District of Kentucky: Fayette, Jefferson, and Lincoln (all
formerly part of Kentucky County) sought on numerous occasions to
split from Virginia, beginning in the 1780s. Ten constitutional
conventions were held in the Constitution Square Courthouse in
Danville between 1784 and 1792. In 1790, Kentucky's delegates accepted
Virginia's terms of separation, and a state constitution was drafted
at the final convention in April 1792. The Virginia General Assembly
adopted legislation on December 18, 1789, separating its "District of
Kentucky" from the rest of the State and approving its statehood.
Kentucky became the 15th state in the Union on June 1, 1792 (after
receiving Congressional approval).
Vermont's admission as a state in 1791 (it was the 14th state, not one of the original thirteen states) was rather complicated (citations omitted):
Vermont existed as a de facto but unrecognized sovereign state from
1777 until 1791. The region had been a subject of a territorial
dispute between New York and New Hampshire during the colonial period,
which royal authorities had resolved in favor of New York; as the
State of New York continued to claim Vermont's territory under this
ruling after independence, the Continental Congress never recognized
Vermont as an independent state. In 1790, after negotiating the common
boundary between the two states, and after Vermont agreed to pay New
York $30,000 New York relinquished its land-grant claim and consented
to Vermont becoming part of the Union. Vasan Kesavan and Michael
Stokes Paulsen assert that, "although Vermont was admitted into the
Union with New York's consent, it is not at all clear that New York's
consent was constitutionally necessary. While Vermont was within the
territory claimed by New York, the preponderance of evidence suggests
that Vermont was not within the jurisdiction of New York."
The formation of the State of Maine proceeded as follows:
The state's exclave District of Maine had proposed secession multiple
times in the early 19th century. Long-standing disagreements over land
speculation and settlements led Maine residents and their allies in
Massachusetts proper to force an 1807 vote in the Massachusetts
General Court on permitting Maine to separate; the vote failed.
Separatist sentiment in Maine was stoked during the War of 1812 when
pro-British Massachusetts merchants opposed the war, and refused to
defend Maine from British invaders. Finally, on June 19, 1819, the
Massachusetts General Court passed enabling legislation separating the
"District of Maine" from the rest of the state (an action approved by
the voters in Maine on July 19, 1819, by 17,001 to 7,132). Then, on
February 25, 1820, the court passed a follow-up measure officially
accepting the fact of Maine's imminent statehood. Maine became the
23rd state on March 15, 1820, as part of the Missouri Compromise,
which also geographically limited the spread of slavery and enabled
the admission to statehood of Missouri the following year.
West Virginia's division was an ad hoc departure not just from the state of Virginia, but from the Confederate States of America which the state of Virginia had purported to join, so it is somewhat of a hybrid between the other purely intra-U.S. state cases and cases like Texas and California that involved a severance of territory from a foreign country. The other three were negotiated in boardrooms. West Virginia's departure was hostile and nonconsensual.
Legally:
Virginia was treated as consenting to the formation of West Virginia
at the outset of the Civil War, even though it was actually a
breakaway, pro-Union province of Virginia that declared itself to be
the lawful government of Virginia and then purported to give
“Virginia’s” consent to the creation of the new state of West
Virginia—which was to occupy that same breakaway corner of Virginia.
Other Article IV, Section 3, Clause 1 Possibilities
The U.S. Constitution authorizes the merger of two or more states in the language above, but it has never happened.
This is, in part, because a merger of two states would reduce the political power of the merging states in the U.S. Senate (in which each U.S. State has two seats), and in the Electoral College (in which in each U.S. State has one delegate per- authorized U.S. Senator and one delegate per authorized member of the U.S. House of Representatives, and the District of Columbia, which is not currently a U.S. State has a number of electoral votes set by the 23rd Amendment to the U.S. Constitution which has at all times since it was enacted been 3 electoral votes).
Article IV, Section 3, Clause 1 of the U.S. Constitution also authorizes transfers of territory between U.S. states and this has happened a small number of times, all in relatively trivial cases involving small acreages of land.
For example, in 1804, Connecticut transferred a small border parcel of land to Massachusetts. Similarly, Boston Corner, in the southwestern corner of the state of Massachusetts, was transferred to the state of New York in 1857, because Massachusetts was unable to administer the hamlet due to geographic barriers that made it difficult to travel overland to Boston Corner from Massachusetts.
Two Step Partitions
There were also several cases in which U.S. states ceded land to the U.S. federal government, the land was managed as a U.S. territory, and then that land later became part of one of more U.S. states. The list below is not exhaustive.
For example, the land that is currently the State of Tennessee was ceded to the United States government by the State of North Carolina on November 2, 1790 (less than six months after it was admitted as a U.S. state under the 1789 constitution), it was then organized as the Southwest Territory, and then on June 1, 1796 was admitted to the United States as the State of Tennessee.
Connecticut ceded some of its Western lands to the United States government in 1800. This land was made subject to the Northwest Ordinance and ultimately was included in some U.S. states.
Georgia ceded some of its Western land in 1802. Some of that land became the Mississippi Territory in 1804. In 1817, this was partitioned into the Alabama and Mississippi Territories and the remaining Mississippi Territory was admitted as the State of Mississippi. Alabama was then admitted as a State in 1819, subject to a boundary adjustment survey between them to correct disputes regarding the boundary which resulting in a peaceful and undisputed mutual resolution of the dispute in 1820.
In 1818, Wisconsin ceded some of its counties to the United States government. They were later incorporated into the State of Illinois by act of Congress. Several of these northern counties in Illinois, including Jo Daviess County, Stephenson County, Winnebago County and Boone County, voted to reattach to Wisconsin, in 1840-1842, but the effort failed.
Modern Developments
While it is not legally required, there is a strong political norm in favor of seeking ratification of any partition proposal in a referendum, and there is not perfect consensus on whether only a statewide approval of that referendum is sufficient, or whether it should be approved by majorities within each proposed successor state. This may be required under some state constitutions. Referendums were held in the two most recent state partitions: Maine in 1820 and West Virginia in 1863. Other referendums have also been held for failed partition proposals. Neither New York nor Virginia, however, conducted referendums in connection with the admissions of Vermont and Kentucky as U.S. states from territory that they respectively claimed, however, in 1791 and 1792.
A California Supreme Court decision, however, recently removed a referendum not preauthorized by the state legislature from the ballot without resolving the legal questions presented on the merits pursuant to a settlement of the parties withdrawing a measure to break California into three states from consideration on the current or future ballots. Planning and Conservation League v. Padilla (Draper) (Cal. July 9, 2018). Those legal questions included whether a referendum alone, not authorized by the state legislature, could propose such a measure.
The general expectation in the non-West Virginia, non-Vermont type case, is that members of Congress from the partitioning state will coordinate the effort at the federal level, and a draft proposal would be prepared by state level officials before Congress or a state legislature will consider it.
Partitions of U.S. states have been proposed, but have not occurred, many more times.
Analogous Events
It is also worth noting that while not strictly within the scope of the constitutional issue, many U.S. states were previously partitioned off from other countries. These provide some precedents legally and practically for how to handle interstate partitions as well.
Alaska was once a territory of Russia.
Texas, New Mexico, Arizona, California, and part of Colorado were all part of Mexico immediately before being a part of the U.S., and Florida was previously a part of Spain.
Louisiana was a French administrative subdivision and almost all of the Mississippi River basin is claimed via the Louisiana Purchase.
Hawaii was an independent Kingdom.
Parts of the Pacific Northwest used to be claimed by the British Crown.
All of the U.S. was claimed by one Indian Tribe or another, many of which had formal treaty arrangements with the U.S. that recognized those tribes as separate sovereigns with territory, most of which were subsequently abrogated unilaterally (which U.S. Constitutional law permits contrary to the way that most countries treat treaties legally and probably contrary to the Founders' intent in writing the constitution) or were modified under duress.
Mexican, French, Hawaiian and British property rights survived the change of sovereign.
Many other U.S. states were previous U.S. territories that were partitioned, often in multiple iterations, before particular portions were admitted to statehood. The example of Alabama and Mississippi described above is one of the first examples of this process.
Practical Considerations When Partitioning A U.S. State
As a practical matter, it is cumbersome to implement and involves mountains of detail, but it can be done.
A map must be drawn and new boundary lines have to have legal descriptions.
There is a divorce-like division of property and debts.
Each resulting state needs a new or amended state constitution and a process to do that has to be determined, and associated Congressional and legislative districts must be drawn.
State seals, flags, symbols, nicknames and other trivialities must be devised.
Usually, the stating point for each resulting state's laws and regulations are the laws and regulations of the shared predecessor state but they have have to be reviewed and many must be rewritten (e.g. myriad statutes and regulations set forth specific details for every county in a state).
Interstate compacts (e.g. regarding water rights) need to be reviewed and often revised.
Somebody needs to figure out what to do with prison and juvenile detention inmates and other institutionalized individuals held in one resulting state based upon convictions in the other one.
Most states have only one capital city holding its legislature building, its state office headquarters (i.e. its state capitol building), its state supreme court, and other statewide institutions, and the architecture, at least, always ends up where it is located. The other resulting state has to decide where to do all of the things that were done for its share of the state capitol bureaucracy and retrieve the records it needs to function from the state capitol.
Most historic U.S. state divisions, logically, can be characterized as spin-offs. The portion of the state that retains the state capitol continues to operate more or less as usual with a bit less hustle and bustle. the state that does not establishes a new set of physical and organizational institutions from scratch, and may receive a credit against its share of state debts for undertaking that burden.
There are literally thousands of detail issues that need to be worked out, often once on a temporary basis and again on a permanent basis, in each state.
Some of the details are typically worked out after the partition becomes official, subject to some broad governing principles and a commitment of all parties to work together in good faith to sort out unforeseen details. Other issues may be resolved in court decisions decades later.
Many federal laws and regulations are likewise specific at a state level and would need to be revised eventually, and new federal officials for each state would have to be appointed or ratified as successors to their previous appointments in a single state.