Not only does the Constitution give the House the power to impeach (and the Senate the power to remove), but it was written before the Twelfth Amendment—when there was a decent chance that, like Jefferson was to Adams, the Vice President would be one of the President’s rivals.
So for all of the carping about “overturning the results of an election,” the Twelfth Amendment makes that much more difficult (Pence would become President); and the Constitution, which was written against a backdrop in which it was far more possible, _still_ says what it says.
(The Twelfth Amendment, a response to the Election of 1800, requires electors to vote for President & Vice President separately. Under the Constitution as written, electors voted for two people without specifying which was which, and the VP was whoever got the second-most votes.)
So now, the winning party’s VP nominee becomes Vice President, as opposed to whoever got the second-most votes. Thus, it’s hard to see how handing the office to the same party’s chosen running mate is overturning the results of anything—especially in contrast to pre-1804 regime.
