More than likely, the tie election would remain undecided after the Electors voted. The Congress meets in joint session on January 6, 2021^ to count the electoral votes (this count happens whether the election is close or not). If no candidate has reached 270 Electoral Votes, then the House and Senate take over and elect the President and Vice-President, respectively. Note that the newly elected 117th Congress will be sworn in on January 3rd, 2021. It is that new Congress that would take on this responsibility.
The Republicans are likely to hold the Senate, and all that the Democrats have to do, is to flip two states to win the Houses' Electoral Votes. The Democrats can flip Pennsylvania, Wisconsin, and North Carolina. This would lead to the Democratic House electing Biden, and the Republican Senate election Pence. But what if the Democrats only flip two of those states? There's an answer for that:
Note that if a majority is not reached in the House vote (e.g., 25-25), that chamber needs to keep at it until the tie is broken. If the deadlock is still in place when the new term starts (noon, ET on Jan. 20), the vice president becomes acting president until such time as the House elects a president.
All Hail President Pence! Granted, this scenario has a low chance of happening, but it is possible. So, NSG, what would you do if Mike Pence became the president, after voting for himself, not once, but twice, first as a voter, and then to break the Senate tie?
I, for one, think it would hilarious. First, Pence was the only one competent in the presidential and vice presidential debates. Second, he has the experience as Indiana's Governor and Trump's VP. Third, it keeps the Republican Populist-Religious Coalition together, without Trump. What's not to like?
What say ye, NSG?