“Well, except perhaps that pesky Constitution.”
Maybe yes. Maybe no. IIRC the COTUS specifies qualifications for President, but not a process and responsibility for validating those qualifications. Also, IIRC the CJ of SCOTUS swears our new President in, right? Is it the responsibility of the CJ to check the qualifications? Is it just always assumed not to be an issue? I just don’t know.
I can tell you that IF in fact Obama is shown not to be a natural-born US citizen as the Constitution requires, and IF he is then sworn in and installed in the Oval Office anyway, then regardless of what any court says (including SCOTUS) the people of the United States will be legally justified in refusing to recognize his authority, and in mounting armed rebellion against the illegal federal authorities.