I'd like to know where this "congress didn't authorize Iraq / Afghanistan " myth came from, but I've heard it no less than 10 times in recent weeks
In any case, if the president asked congress for authorization, and they denied it, an he ordered a strike anyway... THAT would be the coup. The military obeying it would be the illegitimate government.
That said, and it won't make me friends here... I would obey.
Not because I want to go to Syria, but because if it came to a ground campaign, my soldiers would need me