There is a scenario where Obama could not become President but Biden could only be Acting President and not actually President for the duration of the next term if 0 is disqualified after the EC votes and before the Inauguration based on the wording of Section 3 of the 20th Amendment. There would be no President, just an Acting President, because no President would qualify until the next election. Presumably there would be a special election ordered by the SCOTUS, or Congress, but there isn’t a precedent.
I don't think so. If there were no votes in the EC for anyone but BHO, then yes, but there will be votes for John McCain, and possibly, since there are usually a few "faithless electors", for others as well. In fact If I were the Democrats, which I was in high school (Young Democrats), I'd be darn sure there was at least, and preferably only, one other Democrat with one or more electoral votes. Just in case the selection of President is forced into the House. By the Constitution, they can only select from among the top three electoral vote getters, if BHO was found ineligible, that would only leave McCain, unless one or more "Obama" electors votes for someone else, in which case the overwhelmingly Democrat House could select that person, rather than McCain. That person would then become President. But if no one other than BHO and JM get electoral votes, then JM would become President should BHO be found ineligible.