A unilateral withdrawal is well within his authority.
The question is more: Can he develop the wisdom to understand that declaring a date certain guarantees that the folks we tossed out in the months following 9-11 will prevail there and that the rest of the world will suffer from their actions from a safe haven.
The domino theory was correct during the Vietnam era -- fortunately the communist empire collapsed of its own weight before it could go its full route.
It applies very strongly to the current situation. There are many precedents for multi-decade wars, the most recent being the cold war, but earlier, longer examples exist.
Our leadership needs to stay the course -- which means we use timely force, at least the right amount of force (too much is better than too little), and work diligently to ensure our troops are part of the local solution rather than to be seen as the problem. (Not easily done!)