Would you think he had a case?"
President Bush's win was certified by the US Supreme Court (our highest arbiter of the Constitution), was Mr. Obama's eligibility so adjudicated while I was out?
Was Obama sworn in by the Chief Justice? I believe so...
Has ANY case been found to have merit? I thought not...
The military is outside of politics. Let someone else fight it out. Until then, the military needs to assume someone who won the vote, the Electoral College, and is accepted by the Congress and the Supreme Court is, indeed, the lawful President.
There is nothing unlawful about a deployment order. Obey it, or be punished. Or put in your papers and retire ASAP, although he would have had to do that as soon as Obama was elected, since it takes 6 months to retire.