What 90 are you referring to, the training camp roster? I think the GM has final say on the 53, I imagine most teams don't have a QB controversy, so there probably is agreement on QB starter, but that might be where problems may arise.
I have to think, in a normal situation, that the GM and coach discuss difficult roster decisions or at least a direction to go in. But it is the GM's job to give the coach the roster he needs to succeed, then it's the coaches job to make it work on the field. But no doubt in my mind the GM has final say on the 53 and if it came down to it, the game day roster, but I can't imagine too many arguments over game day rosters except for QB. If they disagree too often, then you have problems.