Perhaps you’ll regret this, but you got my professorial juices going. The Constitution originally — something tells me you already knew this— gave the vice-presidency to the candidate with the next highest number of electoral votes. (No popular vote those days.) The screwed-up 1800 election led to the Amendment that gave us roughly the procedure we have now.
It would take an impossible amount of standing on one’s head to immediately make Clinton the next President. But if President Pence, in an always possible fit of bi-partisanship, and as provided for by the 1960s Amendment, nominates her as the new Vice-President , well then —
[You’ll google this, I hope, especially the Amendment numbers.]