This was discussed years ago, when Obama was president, during a previous budget battle.
Things got resolved then , so we never actually have seen a president try to invoke the 14th Amendment for these purposes.
I would not be surprised if Biden does invoke the 14th amendment, from a Democratic perspective, why not try it, it would temporarily delay the issue until the Supreme Court made a ruling and the Democrats could keep on spending until a ruling has been made.
If the Supreme Court rules in their favor that would allow every President in the future to do the same thing, especially the Democratic Presidents.
If the Supreme Court shoots them down, so what we are back to where we are now.