What happened in November 2020 isn't supposed to happen, and hasn't happened in 140 or so years, but back then there were real electoral election issues regarding voter suppression. It isn't supposed to be so easy to try and throw out an election's results. Ultimately, McConnell had control, and he kept the hands on the wheel. He would have been necessary to overthrow the election.
US House of representatives or Senate?
State houses or senates? I still think they wanted to declare some states result illegitimate and keep the rest.
If nobody receives 270 electoral votes, the Presidential election is turned over to the U.S. House of Reps, which chooses, one vote per state, among the three top electoral vote getters. It is the newly elected House, in this case the 117th Congress of the United States which votes.
It's not clear to me what happens in case of a tie, which is actually quite likely. I suppose the House keeps casting ballots until someone gets a plurality
* or until the Inauguration deadline is reached. In the latter case, the Presidency is filled by the newly elected Vice President, if any.
The Vice President, assuming no candidate gets 270 votes, is chosen by the Senate, one vote per Senator, between the two highest VP electoral vote-getters.
Note that Georgia did not certify the election of its two Senators until January 19, 13 days after the Congress passed its judgment on the Electoral College submission, and one day before the Inauguration of President. (Presumably Georgia would have delayed this certification further in the hypothetical.) So the GOP controlled the 117th Senate 50-48 prior to the Inauguration.
The most recent time such a "contingent election" has occurred was in 1836, and that was just for the Vice Presidency, Martin van Buren winning a majority of EV's for President despite the Whigs running four different candidates in four different regions hoping to engineer a contingent election.
One of the most interesting Presidential Elections occurred in 1876. Samuel J. Tilden, Democrat, won 51% of the popular vote and, possibly, a majority of the electoral vote but, as in 2021, some of these results were in dispute. A compromise was reached: Rutherford B. Hayes was named President in return for his promise to remove the remaining federal troops from states which had been in rebellion 12 years before. "Some black Republicans felt betrayed as they lost their power in the South that had been propped up by the federal military, and by 1905 most blacks were effectively disenfranchised by the now-democratically elected state legislatures in every Southern state."
* - The use of plurality to denote "the largest number of votes" is marked by some dictionaries as a USA-ism:
plu·ral·i·ty
/plo͝oˈralədē/
noun: plurality; plural noun: pluralities
1.
the fact or state of being plural.
2.
US
the number of votes cast for a candidate who receives more than any other but does not receive an absolute majority.