Now this depends upon the meaning of “president elect”. I believe it is speaking of the president elected by the Electoral College not the winner of the popular election.
If Obuma is not elected by the Electoral College because he is ineligible then I believe my scenario is possible if not likely. We should remember that political parties have no real say in this under Constitutional theory so the Democrat party has nothing it can do to save its interests.
All of this is obviously new ground with a great deal of murkiness in it.
Section 3. If, at the time fixed for the beginning of the term of the President, the President elect shall have died, the Vice President elect shall become President. If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified; and the Congress may by law provide for the case wherein neither a President elect nor a Vice President elect shall have qualified, declaring who shall then act as President, or the manner in which one who is to act shall be selected, and such person shall act accordingly until a President or Vice President shall have qualified.
So, in the case at hand, assuming 0 cannot produce proof and the EC demands it, the President will not have been chosen by Jan 20, so Biden would be the acting President until they can get a President who qualifies.
I have never heard of any legislation or U. S. Code that covers the situation and authorizes the Congress or anybody else to qualify a President, so if all that actually transpires (unlikely) we would have an Acting President Biden for 4 years. Wow!
I say it's unlikely because if the EC demands proof and 0 doesn't provide proof, then I think the Dim electors in the EC would vote to select Biden as President. Maybe it would devolve to the Senate (the new Senate) to choose a VP at that point.