Unless there is overwhelming proof that Obama is not a natural born citizen, by even the most liberal interpretation of the clause, I simply cannot see the SCOTUS unseating a POTUS. Even if it were proven he was born in Kenya, I could see the SCOTUS refusing to remove him, saying that his mother's citizenship makes him a NBC (I'm not saying I agree, I just think the court might rule that way). From a practical standpoint, I think proof that BOTH his parents were foreign nationals and that he was born outside the U.S., would be needed.
As for impeachment, even if a solid case could be proved, it would require a majority of the House and 67 Senators to vote for impeachment. I just don't see the votes being there, even after the 2010 midterms.
Also, I'm not sure what grounds there are. You can't impeach a POTUS simply for being a fool, with horrible ideas, no matter how dangerous those ideas are. Unless he commits some sort of crime, and leaves behind clear proof of it, we'll have to wait until November 2012 to fire him. And “crime”, does not include signing unconstitutional legislation. The same congress that would be his jury would be his accomplices in that, so there would never be an impeachment on those grounds, even if it were warranted.
The Supreme Court does not have the power to unseat a sitting president. According to the Constitution, it requires a majority of the House and two thirds of the Senate.