My guess would be two words.
Court Martial.
If any of them we're re-instated, or any on Active duty, would be Court Martialed I would imagine that in their defense they would be allowed to supeana the various ultra super top secret documents from Barry's past.
That could be Lt. Easterling's strategy/gamble.
Depends on what they're court martialed for I expect. If someone tried to nail them on Article 88, Contempt Towards Officials, then maybe. But it their commanding officer tells them to deploy and their response is "No, 'cause Obama ain't the president" then I imagine they'll be on the wrong end of a General Court, and they can subpoena Obama's birth certificate till the cows come home and it'll never be allowed.