As to 2008, that's water under the bridge. He's President, qualified or not, removable only via impeachment.
As to 2012, it's a totally different question. Is he qualified to be on the ballot for 2012? Elections are across the fifty states, and they have their secretaries of state.
The Supreme Court might have a role, should they choose to take the right case. But, if I were they, it would have to be slam dunk: Obama was born in Kenya, and not of Stanley Ann.
Not going to happen.
What is going to happen is, Obama is going to carry DC. There will be long faces on MSNBC. Then the Village of South Chicago will regain its idiot, effective the afternoon of 20 January 2013! And Article II will not have had a role!!
The Constitution tells us who can and cannot legally be President. If one "fails to qualify", he/she can NEVER be President. The term "No Person" at the beginning of the eligibility requirements in Article Two is quite specific. It doesn't say "No person, except those who manage to sneak in due to the negligence of Congress". You are saying that there is no such thing as a "Usurper" with your argument, yet, that is what we have here. Impeachments apply to legal Presidents, while a simple arrest will do with a usurpation.
Technically, his right to hold the office of POTUS could be overturned by a writ of quo warranto, but that's not going to happen. And if it did, Obama would not leave office. He'd challenge the court's ruling and stay in office while the lawsuit progressed through the system.