That's the question, after all, isn't it?
Let's say someone with standing ends up placing the several smoking guns squarely on their dais.
The court might ultimately rule that the people and Electoral College ultimately determine an Executive's qualifications, the specifics of the Constitution to the contrary notwithstanding.
This is sort of in line with the legislature (or the Senate or House) prerogative as ultimate authority on the qualifications of its Members.
This would put pressure on Congress to impeach and remove a pretender president, the High Crime and/or misdemeanor being identity theft and fraud.
The real shake then to the social order would be very similar to the long-term damage left by a Senate that turned a blind eye to perjury in 1999.
Then again, the Right Thing for the Supremes to do, the Profile in Courage, would be to view the prima facie evidence as it is, and toss the usurper out of the game.
Not very damn likely, is it?
If a challenge was directly made to Sotomayor’s and Kagan’s positions on the Supreme Court on the basis of Obama’s ineligibility, so that those 2 unconstitutional justices had to be recused, the balance of the court could conceivably overcome Roberts’ sellout to Soros.
Right now Hobby Lobby has the perfect standing to do this, since they have an urgent case, with standing, where Sotomayor very recently caused particularized harm to them. If they have the courage to use Onaka’s verification to AZ SOS Ken Bennett as a basis, they could accomplish this very thing.