This pertains to the United States.
From my understanding (Wikipedia), the House of Representatives can impeach the president with a simple majority. The Senate can then convict the president with a supermajority (2/3 of the Senate). Section 4 of Article Two of the United States Constitution says: "The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors." High crimes and misdemeanors in its original meaning is interpreted as "for whatever reason whatsoever" 1.
Given these facts, it follows that a majority in the House, and a supermajority in the Senate can remove a President and a Vice President "for whatever reason whatsoever".
The presidential line of succession has the Speaker of the House in line behind the Vice president. Normally, if just the President was impeached, the Vice President would take his place, and then nominate a new vice president. However, if the House and Senate impeach and convict both the President and Vice President "simultaneously" (without allowing for the Vice President to ever assume the presidency), then I imagine the Speaker of the House would still be the next in line to assume the presidency (please correct me if I'm wrong).
So--If a single party has a majority in the House, and a supermajority in the Senate, can they replace the president and vice president with the Speaker of the House (from their own party)?
Can't a party that controls the House, and has a supermajority in the Senate always force the president to be from their own party?
As can be found in historical references of the period, the phrase in its original meaning is interpreted as "for whatever reason whatsoever". This phrase covers all or any crime that abuses office. Benjamin Franklin asserted that the power of impeachment and removal was necessary for those times when the Executive "rendered himself obnoxious," and the Constitution should provide for the "regular punishment of the Executive when his conduct should deserve it, and for his honorable acquittal when he should be unjustly accused." James Madison said, "...impeachment... was indispensable" to defend the community against "the incapacity, negligence or perfidy of the chief Magistrate." With a single executive, Madison argued, unlike a legislature whose collective nature provided security, "loss of capacity or corruption was more within the compass of probable events, and either of them might be fatal to the Republic."