If Obama is found to be ineligible then I suggest that there are plenty of Constitutional provisions in place through the 20th and 25th Amendments to deal with it. I don't know of anything that would allow for a new election.
If they discover that he’s not a natural born citizen but do nothing, then it’s up to We the People.
I just don't see that happening because I don't see men like Justice Thomas, Justice Alito, Justice Scalia, or Chief Justice Roberts remaining quiet in the face of a blatant unconstitutional act. If it is proven that Obama is not a natural born citizen then I think the Supreme Court says so, regardless of the consequences. And Obama is removed.
Ok, well, I don’t know what the legal remedy would be or if there is precedent, but if he’s constitutionally ineligible then he should not be allowed to serve. Hopefully these things will be worked out.