What could Iraq look like if we all just left?

Oddly enough, the story of Somalia after the UN withdrew (but before it returned in recent years) shows that power vacuums aren't always to the detriment of society. Of course, the situation in Iraq has significant differences from Somalia- most importantly that a Shiite-dominated centralized government (backed by powerful militias) would at least nominally exist if everyone left. As a result, we would not be leaving behind a true power vacuum, meaning that the group with control of the government apparatus would hold an important advantage over the other groups. This advantage would be enough that the other groups, especially the Sunnis, would have a huge incentive to undermine the government as much as possible, effectively resulting in a civil war.

On the other hand, if we were to combine our withdrawal of forces with an end to most or all international aid to the Maliki government, we would minimize the initial advantage to the Shiites of maintaining a violent grasp on power - in other words, they'd be a government with no money other than what they could get from Iran. As Hamas found out, controlling a government with no money is about as worthwhile as being President of your middle school student council. Indeed, you can't even pay goons to go out and extract money for taxes since they would have no incentive to actually give the money they extract to you.

The only way to make holding on to power worthwhile would be to attract private investors. Even though private investors would love to tap into Iraq's oil, the instability created by a government with no ability to enforce property rights would make access to the oil worthless. Thus, the Shiite government would have no choice but to make peace with the Sunnis, who would find themselves with a surprising amount of leverage to work out a fair deal.

If the government and Sunnis failed to reach an agreement, you would have a state of anarchy - but one very similar to the Somalia example. Of course, the key to all this is that the withdrawal be combined with a complete end to international aid; unfortunately, this is something that most liberals would be completely opposed to on a false belief that the aid would be necessary to prevent a long-term humanitarian crisis.