Uh-oh. All of that indicates we're potentially heading for a Constitutional crisis, if the contested swing-state Republican legislatures & Democrat governors/SoS's choose competing slates.
For the House to be given the responsibility of electing the President, FIRST the Vote Counting Session must rule that no one has a majority. With only two candidates, this can only happen with a 269-269 tie OR if the Congress disallows enough votes to create a no majority situation. With the party makeup of the new Congress (270 Democrats and 265 Republicans) this is not going to happen.
Of course it could happen. First, those specific total counts of Democrats and Republicans you stated are yet to be determined (e.g., two Georgia Senator run-offs). Second, those two totals are irrelevant. If the joint session can't resolve electoral count disputes, then the two chambers meet separately to determine which slate of electors to count for each state with multiple slates. If the two chambers don't agree, then neither slate is accepted and that state loses its electoral votes. And there are other conditional procedures specified as well. Then there's another clause in the EV counting act that says if the two chambers can't agree, whichever slate of electors was certified by the executive of that state must be counted. However, all of that conflicts with the Constitution which says that each state appoints electors in whatever manner the state's legislature directs. So if Republican state legislatures believe it's election fraud, they can pick a Trump slate. Also, there's not even consensus about what "majority" of electors means. If things head in that direction by January, it could be one hell of a mess.
270-265 is a best case scenario, presuming the GOP wins both Georgia seats.
Second, those two totals are irrelevant. If the joint session can't resolve electoral count disputes, then the two chambers meet separately to determine which slate of electors to count for each state with multiple slates.
My point was, the Joint Session WILL resolve any disputes in favor of the Biden slates.