Here’s a better question....
if 0bamao responded affirmatively to a Turkey request that the NTO treaty be invoked, would our military take arms against Israel?
Interesting question. IMO, it depends on how many political, left-leaning, PC generals and admirals currently in uniform.
Either that, or mutiny. It doesn't have to be a public mutiny, of course - it could be all decided within the Oval Office.
Considering that Israel has nuclear weapons, the possibility of the USA waging a war against Israel is very low, IMO. Obama will not issue an order. If the Turkish ship is destroyed and all on board killed (including the Turkish Prime Minister) NATO could tell Turkey that there is nothing to do until someone invades Turkish land. I doubt that NATO mutual defense agreement will kick in if a NATO country invades some other country and the invasion forces get what is due. Some countries still defend their borders, though that art is largely lost in the USA.