Actually, thanks to the MSM's singleminded pursuit of putting Obama in office, it was only well known among news junkies like us. The average voter had utterly no clue then, and has no clue now. That would be entirely different if he were a Republican; the MSM went after the non-issue of McCain's citizenship two or three times. But it is what it is.
I think the only type of action that has even a small chance of getting to SCOTUS is a challenge to his military authority or a challenge to a law he's signed. The former is already underway.
Interesting that you think that. How about an action challenging the legal efficacy of an action required by the Constitution to be performed by the "President"--such as the appointment of a Supreme Court Justice? An action in the nature of a Quo Warranto challenging the authority of the Justice to sit on a particular case?
Observe that a number of military officer challenges to existing orders have been filed but so far, no one has been able to get one to issue. At the point where that case reaches the judge, they withdraw the order and moot the challenge.