What Happens if the Vice-President Steps Down?

There has been a strange rumor that Vice-President Harris may resign. I have no reason to credit the rumor; but it does raise a rarely-discussed question (which a reader e-mailed me about): What happens when a Vice-President resigns—or dies or is impeached, or for that matter leaves office to become President—and in particular what happens when there's a 50-50 senate?

For much of the nation's history, there was no provision for such situations, and as a result the Vice-Presidency was fairly often vacant (chiefly as a result of the Vice-President becoming President, except once when Vice-President John Calhoun resigned). But the Twenty-Fifth Amendment provides:

Whenever there is a vacancy in the office of the Vice President, the President shall nominate a Vice President who shall take office upon confirmation by a majority vote of both Houses of Congress.

(This was how President Gerald Ford became Vice-President, after Spiro Agnew's resignation.) This provision yields two obvious follow-up questions, especially when the Senate is divided 50-50.

[1.] If the Senators are tied, would Vice-President Harris be able to break the tie to approve her own replacement? No, I think: No vote can happen (indeed, no official nomination can happen) until there is a vacancy, so by definition either

1. the Vice-President is still in office, in which case there can't be a vote, or
2. the Vice-President is no longer in office, in which case she can't break a tie.

[2.] Can the President pro tempore of the Senatebreak the tie? The Constitution provides that "the Senate shall chuse their other Officers, and also a President pro tempore, in the Absence of the Vice President, or when he shall exercise the Office of President of the United States." But I don't think this has been understood as allowing the President pro tempore to cast two votes, both his own and the Vice-President's, and have those count towards "a majority." When 100 Senators are voting, and the Vice-President is not, a 50-50 vote is not "a majority."

Of course, there may well not be a 50-50 tie even if the Vice-President resigns; after all, if there's no Vice-President, then under the Presidential Succession Act, Nancy Pelosi (the Speaker of the House) would become next in line for the Presidency. (Some argue that the presence of the Speaker of the House and then the President pro tempore of the Senate in the succession is unconstitutional, but even if that's so, then Secretary of State Antony Blinken would become next in line.) It's not clear why Republicans in the Senate would necessarily prefer those as potential Presidents over someone President Biden proposes.

But I suppose President Biden could nominate someone whom the Republicans may sufficiently dislike. And I suppose that in any event Republicans might even refuse to confirm a Vice-President chiefly out of concern about the Vice-President's tie-breaking power (no Vice-President, no tie-breaker for votes over ordinary Senate matters, such as on legislation) rather than about the possibility of the Vice-President succeeding. Both highly unlikely, I think, but stranger things have happened ….

Yet again I stress that this is just constitutional lawyer fun: I have no reason to believe that the Vice-President actually has any plans to resign.

UPDATE: See also this follow-up post, Can a Vice-President Be Confirmed by a Majority Vote of Both Houses Put Together?