"The Electors shall meet in their respective States, and vote by Ballot for two persons, of whom one at least shall not lie an Inhabitant of the same State with themselves."
the restriction is that, in the electoral college, electors can't vote for both a president and a vice-president from the same state as the elector. not the same state as each other -- all three have to be from the same state for it to be a problem.
so if the president and vice-president on one ticket are from the same state, then for the electors from the rest of the country, this is no problem because they're voting for two out-of-staters. it's only a problem for the electors from the same state as both the president and vice-president. in that state, they would vote for the president and vote for some random out-of-stater for vice president (essentially throwing away that vote).
so the presidential election would not be affected, but the vice-presidential race would. this is only a problem in a very close race where that one state made the difference. in which case the president would be elected as normal but there would be no vice-presidential victor as neither candidate had the required 270 electoral votes. in which case the election would be thrown to the house of representatives. in normal times they would likely let the president have his own vice-presidential choice, given that that was apparently the peoples' choice as well, but in these hyper-partisan times it's conceivable that they'd give it to the other guy or even to someone else entirely.
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