Sam Spade has had a lot of action on his thread for the tied Electoral College. I didn't want to clutter it up with this thought, so I like to start a new line of discussion. Let me start with the key part of the 12th Amendment:
In a tied EC, the Democrat should win based on the likely composition of the state delegations. There might be pressure on some House delegations to side with the winner, but the Democrats would not want to vote for McCain. So instead an elector (or two) is convinced to write in a compromise Democrat (Al Gore for instance). Since three choices for President go to the House the compromise is an eligible candidate. Some Republican-dominated house delegations recognize that McCain cannot win, and don't want Obama. So after some lobbying a bipartisan coalition of states elects the compromise before the constitutional deadline.
There are a lot of what ifs here, but the questions for a tied EC are:
Could one or more electors be convinced to offer a compromise candidate?
Who would reasonably fit the bill as a compromise?
What coalition of states could agree to the compromise candidate (or is it President Biden)?