[Non-Sequitur]

But if Obama was not eligible on the date when a new administration was to take office, then my guess is that George W. Bush would still be President until such time as a replacement can be elected and take office.

And what clause of the Constitution do you base that on?

[William Tell]

Non-Sequitur said: "And what clause of the Constitution do you base that on?"

Oops. Can I have a do-over?

The Twentieth Amendment appears to address the issue: " [...], 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; "

So, Biden it is.