Since Obama’s father was already married when he married Obama’s mom the marriage was probably not legal. That would mean while his father wasn’t a US citizen his only “legal” parent was. Even if he was born outside the US because of his American mother he’d be a citizen (see Montana v. Kennedy http://caselaw.lp.findlaw.com/cgi-bin/getcase.pl?friend=nytimes&navby=case&court=us&vol=366&invol=308&pageno=314) but he’d be a “citizen by birth” not a “natural born citizen” The question if he was not born in Hawaii like some have speculated is a “citizen by birth” eligible. It’s never been adjudicated and our current Supreme Court would probably decide he’s eligible with Kennedy providing the swing vote.
Personally I think this is an exercise in barking up the wrong tree and I’m not going to get to excited about the birth certificate issue for now.
I think Obama is reluctant to produce a birth certificate because his parents were never married—legally or otherwise (since his father was already married).