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.
“...is shown not to be a natural-born US citizen as the Constitution requires...”
There’s the rub. How do you prove a negative? Another way to ask the question is “who holds the burden of proof?”
I just don’t think the COTUS covers this.