Following the 2003 U.S. Invasion of Iraq, the country is divided in two new countries; one Sunni and the other Shia. The Iraqi Kurdistan is denied independence and is instead annexed by Turkey.
Probably even GWB would understand this being bad bad idea. Americans need strong country against Iran and it not help that you divide rival of Iran as two nations. North Iraq would be pissed that it is enforced as landlocked nation and South Iraq would shift soon under Iranian influence. This just would create more problems as it would solve.