Interesting that you think that. How about an action challenging the legal efficacy of an action required by the Constitution to be performed by the "President"--such as the appointment of a Supreme Court Justice? An action in the nature of a Quo Warranto challenging the authority of the Justice to sit on a particular case?
Observe that a number of military officer challenges to existing orders have been filed but so far, no one has been able to get one to issue. At the point where that case reaches the judge, they withdraw the order and moot the challenge.
That's way above this layman's head. I was voicing my opinion based on the fact that obviously no court is going to take up the issue based solely on, "Hey, he shouldn't be president." A challenge to some action of his is required.
Maj. Cook was a reserve officer and could have his challenge to Obama deemed to be a retraction of his voluntary offer of deployment.
In case you missed it, the just announced challenge to Obama’s proofs of eligibility by Lt. Col. Terrence Lakin, D.O., an active duty officer, won't be able to be dismissed on that basis. If subjected to court martial, Lakin appears to intend to put the burden of proof on Obama in a quo warranto filing.