en.wikipedia.org
"The three past contingent elections were held by the outgoing Congress, since, at the time, congressional terms ended / began on March 4, the same day as presidential terms. In 1933, the 20th Amendment moved the congressional term end / start date to an earlier date in the year than the new January 20 presidential term end / start date. The amendment reduced the length of lame-duck sessions of Congress. As a result, the contingent elections are conducted by the incoming Congress.[2]"
I made a map of the state house delegations for the incoming congress. Note that we flipped the Iowa delegation red this year, and turned the Minnesota/Michigan/Pennsylvania delegations into tied delegations.
Because each state will be voting as one bloc, I'm not quite sure how the tied states would play out if the Repubs and Dems in those states can't agree on a candidate. However, if at least 26 out of the 27 GOP controlled delegations votes for Trump, I suppose that would be moot. The question is...is it possible for enough delegations to cuck out and give it to Biden? That seems unlikely to me, because let's assume that all 20 Dem controlled delegations try to give it to Biden. They need 6 more, so let's assume that one Repub in each tied state cucks out for Dementia Joe. That leads to 23 House delegations giving it to Biden, which means they'd need at least 2 more. The most Dem optimistic outcome I can think of in this scenario is something like the Utah delegation and maybe the Wisconsin delegation (or maybe one of the states with only 1 Repub congressperson) cucking out on top of that for Joe. But it seems all that's a tall order.
The most likely outcome in this scenario, I think, would be all 27 GOP delegations voting for Trump, but enough of them would probably try extracting GOP-establishment friendly concessions from him beforehand.
Oh, and I think the Senate would easily select Pence as VP in this scenario as well.
NOTE: This all only happens if neither candidate gets over 270 electoral votes. Also, the only choices the House can make are among the Top 3 electoral vote getters, which means that for example (hypothetically speaking) if 1 Faithless Elector casted a vote for Bob Chipman out of pity, leading him to be 3rd place in #of electoral votes, and 26 House delegations voted to make Bob Chipman the President, we'd have President MovieBob (despite him presumably getting 0 popular votes).