Anyone seriously considering this is sorely mistaken.
When dictators consolidate their power, they purge their administration of anyone who does not pledge their supreme loyalty to them. The principled ones of course quit immediately, but without a doubt there will be significant number of people that remain. They are only human, and they have to deal with exactly the same problem that anyone else quitting their job faces in America today. Their minds will rationalize the actions, the Dictator will provide ample bogeymen as targets of hatred.
And even if they DO disobey an order, an American where the military no longer obeys the Civilian Administration... however terrible that might be, would be a dangerous line to cross. All bets are off at that point: the American military is the largest, best equipped fighting force the world has ever seen. Whoever commands it instantly commands immeasurable amount of power.