If they were given orders by someone -- anyone -- placed in a position of authority over them and they refused to obey they would be charged and punished for failing to obey a lawful order.

If they then incited others to disobey the lawful order they could be charged with inciting mutiny.

If they...well, the punishments range from fines and/or stockade (jail, gaol) time to death.

Refusing to obey an order would normally get you an "Article 15" -- nonjudicial punishment. A fine, a bust in rank, confined to quarters, that sort of thing.

A court martial is needed for greater punishment and a general court can punish by execution if need be. I believe the current death sentence in the military is by lethal injection. This would be done at the Fed. Prison in Terre Haute, Indiana (where Timothy McVeigh was executed). The President, as Commander-in-Chief, must approve all death sentences.