No, there is no burden on Obama to do anything at this point.
Look, you can't just throw stuff out there and say it has to be a certain way, just because you say so. This is the basic point both I and NS are making here.
Where is the law? If you want to claim Obama has to fork over a specific document, show the law that says that very thing. If you want to claim he has the burden of proof, show the law that says that. Otherwise, you shouldn't make those kinds of claims. That's all.
The easy to understand words of our Constitution have been posted on this thread repeatedly. I can't help it if you choose to ignore them.
"No person except a natural born Citizen...shall be eligible to the Office of President...."