I believe that if Obama is found to be ineligible then his whole team would also be ineligible. They would lose by default, and McCain/Palin would be the winners. If that’s not the case it should be the case.
We would be stuck with Biden or Pelosi, however, since Pelosi signed off on nomination forms declaring Obama as eligible, she could also go down with the ship. I forget who is next in line. Ultimately, we’d be left with a substitute who would be nothing more than a really lame duck until 2012.
That belief is not based in law or the Constitution. The former doesn't speak at all to this issue, and the latter is maddeningly vague on this specific point.
The actual, legal realities are:
The problem is what to do if Obama is found to be ineligible. Becoming ineligible is simple enough -- the President is removed and the Vice-President takes over. I.e., President Biden, who would then nominate a new Vice-President, to be appointed with advice and consent of the Senate.
Of course, if Obama had been found to have been ineligible prior to Congress' ratification of the Electoral College vote, the matter would also have been simple (Constitutionally, though certainly not palatable to the Democrats), then no (valid) candidate would have achieved an Electoral College majority, and therefore the House of Representatives would have to select one of the top 5 (valid) people having received Electoral College Votes. But there was only one person who qualifies under that scenario: John McCain, who would be President with Joe Biden as his Vice-President.
The problem arises in that the Constitution makes no provision for when a sitting President becomes ineligible because it was shown that he never was eligible in the first place. In this case, it would likely be up to Congress to deal with the matter (as they are the judge of elections and nothing in the Constitution would restrain them, apart from the actual eligibility requirements). I would expect that they would do the most politically expedient thing: declare the office vacant, and then proceed as in the first scenario above with President Biden.
That's not the case. But you're entitled to keep hoping.