What Obama needs, is a birth certificate showing some other guy as his father. Of course, then his entire life story is exposed as a lie, but (perhaps) he could show himself as eligible.
There is no really good outcome for Obama. His best bet is to have an invisible BC, and to say "It's all good" -- and that is the game he's been playing for years. It works for him. As soon as the BC becomes visible, then the data on the BC comes into play. And then it's over for him.
The problem with that line of argument is that a definition of "Natural Born Citizen" does not exist. There is common law, court precedent, etc. But no clear definition.