“The person having the greatest number of votes as Vice-President, shall be the Vice-President, if such number be a majority of the whole number of Electors appointed, and if no person have a majority, then from the two highest numbers on the list, the Senate shall choose the Vice-President” - 12th Amendment
But it's not a simple vote, right? Each state gets 1 vote, not 1 per representative. A numerical advantage in representatives might not matter then. For example in states like my own state of NJ its obvious the result will be a vote for the democrat. And in Alabama you'll get a vote for the Republican. But in states where there are a more even mix of parties could end up voting democrat. Also some states have very few representatives but since all states get a single vote, they get a much higher influence on the outcome than usual. Think Maine, for example, which has only two congressional districts; in a simple vote they are 2 votes 535 but in this scenario they are 1 vote out of 50.
I haven't done the analysis to see how many such states exist but if it's enough the vote in congress could still go to Obama.
The members of the Electoral College will know going in the expected result, and enormous pressure will be put on individual electors to switch. If all hold to their party, would not be surprised if the D’s play a new game - all their electors swap the P and VP roles so Obama is their VP choice, thus the winner of the VP slot if the new Congress is controlled by the Democrats (including with Biden presiding over a 50-50 split).
Life could be very interesting - all the more reason to work our hardest to make sure it’s not even close.