It may ultimately fall to the military (who deserve to have a Commander In Chief who is in fact eligible to serve in that honored position and is legally capable of issuing lawful orders) to utilize the Uniform Code of Military Justice and demand that Obama establish the facts.
May I suggest Section 935. Art. 135. COURTS OF INQUIRY and possibly
Section 883. Art. 83. FRAUDULENT ENLISTMENT, APPOINTMENT, OR SEPARATION
Any person who—
(1) procures his own enlistment or appointment in the armed forces by knowingly false representation or deliberate concealment as to his qualifications for the enlistment or appointment and receives pay or allowances thereunder
[links provided at the bottoom of article]
The President is not Subject to the UCMJ.
That said, the very first law enacted by the first Congress was to codify the Declaration of Independence. IOW, the people have a legal right to overthrow the government and the Constitution bars the armed forces from getting involved on either side.
Get several hundred thousand patriots to march on Congress when Obama gives his state of the union address, and something could be done in a hurry. I don’t mean just marching on Congress, but marching into the House Chambers; in a non-violent manner, of course.