His effort will be half-hearted, no matter what he says.
Don't be quick to say that unless you've actually spent significant time in the Big Green Machine. I was handed many orders that I thought were ill-advised, foolish, et cetera. The one time that I didn't obey the order and try my damndest to make it come out in synchronization with the commander's intent was when it was both morally and legally wrong. (Morality and legality of orders tends to line up very nicely in the US military--it's nice being one of the good guys.)
The military is all-volunteer. I'm of the opinion that if a service person cannot support a military effort, and makes that known, he should be shown the door.
There ARE grounds for separating the person under those circumstances. To wit, he is definitely in violation of Article 88 of the UCMJ (contemptuous speech towards or about public officials).
And discharged dishonorably.
Article 88 can easily get you six, six, and a kick (confinement at hard labor for six months, forefeiture of pay and allowances for six months, and a dishonorable discharge).
By the way, Poohbah, it's now a DD, total forfeitures, and a year.