Given the Sunnis have a monopoly on conventional military competence, have hundreds of thousands of indoctrinated competent veteran fighters at war and domestic 'pacification' operations which included ethnic cleansing and genocidal acts, have a strategically brilliant Jordanian ally (Zarqawi) at waging a war of the flea against a super power as he did against the Soviets and you just told the Sunnis no oil money for them you now own a big stand pile you have just managed to provide virtually all Sunnis a far greater incentive to support the post Saddam fight.
If the U.S. isn't willing to take a lot more casualties then OTL the jihadists and Sunni members of Saddam's various military and terror organs take all of Iraq in a war of annihilation and given the level of Shia and Kurdish military competence at the time they would win and large parts of Iraq would be depopulated.
The only question is after where they take their war next Iran or Syria.
The central problem in Iraq is you have a minority that Saddam radicalized into rather extreme religious ethno-nationalism, but even beforehand was used to ruling Iraq for generations and knew how to do it using terror on an epic scale and kept the understanding of how to run a state and an army for their own community.
The Shia and Kurds of 2003 were far less competent then they are today about running such things or managing military affairs, they still aren't as competent as say IS right now in how to run an army, but are catching up over time.