Are we sure about that? The 12th says "majority of the appointed votes". If 62 EVs are tied up (20+16+16+10=62), then there are only 476 EVs appointed. Biden needs only 239 in that case... and he would have that even without WI, MI, GA, and PA. 306-62=244. NEV, or NH + NEB CD2, would need to fall unexpectedly after the clock has expired. (Each has strong circumstantial evidence, however.)
Either that, or a shocking number of Faithless Electors come to rescue the nation and the world.
That's not what the 12th says.
This is the pertinent text:
--the person having the greatest number of votes for President, shall be the President, if such number be a majority of the whole number of electors appointed; and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President. But in choosing the President, the votes shall be taken by states, the representation from each state having one vote;
So it's the majority of the electors appointed.
The idea here is that ALL 538 of the electors are appointed prior to Dec 14th...but not ALL of their votes are transmitted to the President of the Senate and the Archivist by Dec 23rd due to any number of reasons (tied up at the state legislature level and miss their deadline, tied up in the courts and miss their deadline, etc).
Therefore, the need to get to 270 still stands and with enough states not resolving and therefore transmitting their votes from their already appointed electors, nobody gets to 270 and it goes to the House for the 1 vote per state provision.