“c. they resigned”
And that is about the only way an officer is going to be able to refuse the orders of the President.
Think of the common sense argument here: If the Supreme Court, Congress, and the military Chiefs of Staff recognize Obama as the ligitimate President, what chance does a Major have in refusing his orders?
What if others follow the Major?
Major Cook has not refused the order...he merely sought confirmation of it's legality, as is his duty when receiving an order he perceived to be of dubious legality. From all I've read, Major Cook is willing to comply with his deployment upon confirmation of it's legitimacy. Lt. Calley was destroyed for not having done the same thing 40 years ago.
As a former officer who resigned my commission in disgust during the Clinton years, I have a fair degree of sympathy for Major Cook, and believe he's acting out of genuine conscience and not for self-aggrandizement or cowardice. It seems to me that if we don't expect our officers to act in a like manner, we need to stop wasting time teaching legitimate avenues of dissent and professional ethics in our commissioning sources.