All it takes is 1-2 unfaithful electors in the Electoral College in a close electoral race to throw it to the House, which is allowed to consider the top three. If that happens, the Senate is only allowed to consider the top two. I don’t know if the Vice-President gets a vote in case of a tie in the Senate.
The Senate only votes for the VP guy (top two).
You should note....in the House, where they vote for the President and the top three...they must vote as a state. So if there are six representatives from that state (3 Dem and 3 Rep)....unless there is some agreement, there is a balanced vote, and the state’s vote is worthless. Last time I counted, there were eight states where it’s balanced out. So you’d could be talking about a pretty simple vote and taking less than 30 minutes to accomplish.