This is going to be hard for the Obama truth squad to answer. Besides the factual problems, there is a natural human tendency to crave wicked conspiracy theories that explain or solve much with only one or a few explanations.
I don’t know if anyone has mentioned it, but this may be a fishing expedition by the Obama afectionados. The bait is he is not a legitimate candidate. They could let the the conservatives run with this and then set the hook suddenly by providing the original birth certificate. This proof of the right being wrong would make a terrific slogan in some way to obviate any and all rumors.
A better tactic on our part would be to wonder, “why Obama and his supporters don’t put this rumor to rest...” Tacitly assuming his claims but questioning why he cannot easily and quickly answer evidence to the contrary would be a better tactic in IMHO.