besides the president isnt the supreme power of the country and military.. tony blair holds more control over britain and its military then george bush does over america and its military.
The president is Commander in Cheif of the US millitary. He is the head of their chain of command. I'd say he holds quite a bit of control.

On topic, I think we at least need to set a solid deadline for a pullout. Maybe it'll give the Iraqi government an incentive to stand on it's own feet. I don't propose leaving without warning and letting the country collapse.