If the Vice President dies or leaves office early, the President is not required to pick a new VP, making the Vice Presidency vacant. Does this mean that a presidential candidate does not have to pick a VP candidate for the election?
- The Constitution says electors vote for both President and Vice President
- 3 U.S. Code § 7 says electors vote for both President and Vice President
- Some states have "candidates for President and Vice President" in their election laws
- It's never been done so the above election laws are untested
- It's never been done so the response of voters is unknown
There do not appear to be any actual hard requirements, but the Constitution and 3 U.S. Code § 7 do seem to have implied requirements that some may view as requiring a candidate for Vice President. And some states may have hard-but-legally-untested requirements.
There appears to be a "real world" requirement to have a candidate for Vice President, and various state ballot laws effectively place a national deadline for the selection of a Vice Presidential candidate (and a Presidential candidate, too) in August prior to the November election.
And candidates get their names in the news and free time to spread their message from the events in the selection of a Vice Presidential candidate.
Every major party that's serious about winning a Presidential election will also have a Vice Presidential candidate despite the apparent lack of any explicit hard requirement.
The Constitution specifies electors vote for both a Presidential and a Vice Presidential candidate. Per the 12th Amendment:
The Electors shall meet in their respective states and vote by ballot for President and Vice-President, one of whom, at least, shall not be an inhabitant of the same state with themselves; they shall name in their ballots the person voted for as President, and in distinct ballots the person voted for as Vice-President, and they shall make distinct lists of all persons voted for as President, and of all persons voted for as Vice-President, and of the number of votes for each, which lists they shall sign and certify, and transmit sealed to the seat of the government of the United States, directed to the President of the Senate;
3 U.S. Code § 7. Meeting and vote of electors specifies the date:
The electors of President and Vice President of each State shall meet and give their votes on the first Monday after the second Wednesday in December next following their appointment at such place in each State as the legislature of such State shall direct.
There are 51 separate elections held, one in each state and the District of Columbia, with each having different laws covering the elections. California apparently does not have an explicit requirement for a Vice Presidential candidate, But Texas does. New York does, too, explicitly specify the Vice Presidential candidate.
Those ballot laws appear to be legally untested should a Presidential candidate try to run without a Vice Presidential candidate.
As far as when the candidate must be identified, New York requires that be known 55 days before the election, for Texas the number is 71 days - or the first day after the final day of a party's national convention.
Given such variation between states requirements for getting candidate names on state ballots, there appears to be effectively a requirement that the Presidential candidate and party decide on a Vice Presidential candidate by about two months prior to the election, which means early September. The historic normal August-ish dates for national party conventions are all consistent with an effective early September/late August deadline for selection of a Vice Presidential candidate.
There doesn't seem to be any provision at all for there being no candidate for Vice President. The laws of Texas, for example use phrases such as "party's nominees for president and vice-president". Would a party that only submitted a candidate for President comply with Texas law? Answering that question for the laws of every state is probably more suited to Law than it is to here. As far as I know, there is no precedent at all for party having a candidate for President without having a candidate for Vice President.
Since it's apparently never been done, I doubt any Presidential candidate or party would want to risk not appearing on state ballots should an anomalous situation arise where a party and its Presidential candidate decide that they'd be better off without a Vice Presidential candidate.
And it's important to remember that the process of selecting a Vice Presidential candidate is used by candidates and parties to get their names and messages out in news broadcasts and articles.
So, while there doesn't seem to be an actual national hard requirement for a Vice Presidential candidate, there may be multiple state-level ones of untested rigor where violating ballot requirements may be risky - Texas definitely appears to be in this category. No serious candidacy for President would risk forfeiting Texas electoral votes.
And the fact that it's never been done in and of itself adds risk. How will voters respond when they actually cast their ballot? "Joe Schmoe not having a VP candidate is weird." sure seems a lot more likely than "I'm voting for Joe Schmoe because he didn't pick a VP!"
Another risk also exists: the Speaker of the House is second in the Presidential line of succession. Without a Vice President, the Speaker of the House is next in line. Not having a Vice President increases the chances of handing the Presidency over to "that other evil party".
Bit of trivia context;
Upon founding of US constitution the VP role went to the candidate with second most votes in the general election. Then the 12th amendment of 1804 required to cast a separate vote for president and VP.
But until the 1960's VP's were chosen by the candidate and party, not necessarily before election. Therefore in short, the answer is No, a presidential candidate is not obligated to have a running mate, but it is mandatory as per constitution to have a VP when serving.
As for the replacement, History.com explains:
Prior to the ratification of the 25th Amendment in 1967, there were no official procedures for filling a vacancy in the vice presidency. If a VP passed away or moved into the Oval Office because the president died, the veep slot would stay empty until the end of the presidential term. Before 1967, eight presidents and seven vice presidents died while in office, adding up to a total of some 37 years that the U.S. was without a VP. (Today if the VP office becomes vacant the president nominates a successor who then must be confirmed by a majority of both houses of Congress.)
Unrelated but a hopeful prospect in these polarized times:
In 1864, in the interest of fostering national unity, Abraham Lincoln from the Republican Party (popular in the North) and Andrew Johnson of the Democratic Party (popular in the South)