This is the very reason that we should instead go back to the original system where the Senate chose both the President and the VP.
Our Founding Fathers were smarter than we realized.
Uh, when did the originally system ever have the US Senate choose both the President and the VP??
Really, it never happened. The electoral college has always picked the President and Vice-President. When there was no majority or a tie, then the House of Representatives, with the States each having ONE vote chooses the President, and the Senate chooses the Vice-President.
When did the senate pick the president?