But they could rule that he is not, and never was eligible, and thus was never POTUS.
Only the President, Vice President and all civil Officers of the United States may be impeached. If he's not President, he can't be impeached. Besides which, is being ineligible Treason, Bribery, another high Crimes or Misdemeanors.
I'm being a little flippant, but it is uncharted territory. The founders neglegeted to say how someone who slips by, but is discovered to have been ineligible, is removed.
This is where we musty sadly part legal company. He is exercising every prerogative of the office. He is the CIC. He is the de facto POTUS, and is, running the military, our foreign policy, and as is painfully obvious, the country. I have no doubt that he is ineligible. De facto, not de jure.
He cannot be removed except by impeachment and conviction in Congress. If the the SCOTUS rules on the appeal of the Writ of Quo Warranto, and finds him indeed to to be ineligible, they cannot order his removal.
That still is the sole prerogative of Congress. They may, or may not use the SCOTUS ruling in anyway they see fit.
Think of a real estate transaction, in which you take title to a home with a non-disclosed flaw. Your real estate agent failed in his due diligence. You own that property. You can sue the former owner who knew about the problem, you can sue your real estate agent for either knowing and not disclosing, or even for never knowing, and you can win. You will be made whole. But the house remains yours. Obama is your house. You will win, but in a time frame not to your liking, perhaps well after 2012 has come and gone.
We have lived to see a temporarily successful, anti-constitutional coup. If we are tempted to solve it by extra-constitutional means, we would be just as bad as Obama.
Concentrate your considerable energies on getting the GOP in shape to hobble the usurper in 2011 1nd 2012.