Let's start out by assuming that the dream of building a new, better, and democratic Iraq has pretty much fallen by the wayside. That being the case, we're left with a messy situation and we have to find a way to salvage whatever we can for the Iraqi people and for the interests of the United States and other involved nations.
Right now, the problem with Iraq is that the Shiites are winning and that means that Iran is winning. If we were to pull out of Iraq today the Maliki government would bring in full scale Iranian support and crush the Sunnis. Kurdistan would become independent (the one bright point) because the Iranians know better than to try to fight the Kurds, but the rest of Iraq would become an Iranian puppet state. Once they consolidated their gains the Iranians would then move south and seize the oilfields in Kuwait and Saudi Arabia and perhaps even the United Arab Emirates, just as Saddam attempted to do. Unlike Saddam, the Iranians would be competent and the bruised and bloodied US, having already written off involvement in the area, would not intervene, so the Saudis would pull back into the desert and be virtually unable to fight back.
The upside of this would be a guaranteed holy war between Sunnis and Shiites all over the region, mainly taking the form of terrorist attacks against Iran, which would be a nice change of pace. The downside would be that the Iranians would have an empire, controlling most of the oil in the Persian Gulf and wielding enormous international power. Once they consolidated their gains, their oil wealth and enlarged territory and population would make them a major player in world politics and the international economy at least on a par with India or any of the major European nations, and probably more powerful economically. Their victory would also establish a real legitimacy for Iran as the premier state in worldwide Islam and they would likely have a claim on the support and resources of a network of other nations from Indonesia to Morocco. They would be the new Caliphate that so many Muslims have been yearning for.
That future of a super-powerful Iran is what we here in the 'Great Satan' really want to prevent the most – far more than we want to help the Iraqis or protect the flow of oil. Without a draft we don't have the manpower to increase our presence in Iraq or fight Iran directly, and financially we really can't afford a unilateral war with Iran, even if it's fought through surrogates. That means we can't stay in Iraq forever or escalate our efforts enough to make Iraq stand on its own. The question we face is how do we stop Iran if we write off Iraq and our involvement there.
One radical solution which no one has suggested yet is to get someone else to do our dirty work. You might wonder who on earth would want to take up the financial and military burdens of fighting Iran in the Persian Gulf. Certainly no one would want to do it for the quasi-altruistic (dumb and idealistic) reasons which motivated the US to get involved, but there are countries which might do it out of that most powerful of motivations, self-interest.
Saudi Arabia has already indicated its intent to resist the expansion of Iran. They have been doing this with financial and material support for Sunni militias in Iraq, and through their alliance with the United States. They know that with the US out of the picture they would be in serious trouble, and although they have a fine military they just don't have the manpower to actually go toe to toe with Iran. It appears that as US resolve weakens and the situation in Iraq worsens, the Saudis are shopping around desperately for another solution, to essentially buy their way out of trouble with their vast financial resources.
What the Saudis need is a country with a lot of soldiers and desperate need for oil, which would be a perfect description of China. China is anticipating an enormous oil shortage as a result of its growing industry and population, a shortage like nothing the world has ever seen. It's the one thing standing between them and what they perceive as their economic destiny. China has the largest army in the world with 2.8 million soldiers. They aren't the best trained or equipped, but there are a hell of a lot of them. The Saudis have the oil the Chinese need and the money to outfit at least part of their army with more modern hardware, and the Chinese would have none of the manpower problems the US has had. If doubling the troops in Iraq would solve the problems there, well that's just 1/10th of their available forces.
The Chinese have more than just the need for oil to motivate them. They've already got problems with domestic Islamic minorities like the 16 million Uighur in Xinjiang province who could easily fall into the Iranian sphere of influence. They don't much want a huge theocratic empire controlling most of the world's oil and sitting pretty much on their western border.
This isn't something the United States could do on our own, but we could certainly act as a matchmaker to bring Riyadh and Beijing together for their mutual interest. So why not invite the Chinese into the Persian Gulf? Offer them control of the Iraqi oil fields, with a certain amount to be paid to the people of Iraq, along with the requirement that they provide security for the region, which means putting Shia-dominated southern Iraq under the control of the Chinese Red Army. This would essentially be another partitioning plan, with the Sunnis retaining control of the 'Sunni triangle' with the help of the US and other international forces, but with the added clout of the Chinese thrown in. And while the Red Army may not be as well trained as the superb US military, they likely have more experience and more appropriate training for suppressing unruly civilian populations which is something our military just isn't trained to do.
You could start a plan like this out relatively subtly. Instead of offering the Iraqi oil contracts to various multinational oil companies, you offer management of the oil fields and disposition of their output to the China National Petroleum Corporation. Since they're a Chinese company they're largely state owned, which means from the very start they're going to bring in the Red Army to provide security. And to be secure they need to control more than just the oil fields. They need to control Basra and the other ports and they need to establish a secure perimeter, which means controlling a lot of territory around the oil fields and refineries.
They also need to stop terrorist attacks on the infrastructure, which means subduing the terrorists in the region and establishing an extended secure perimeter. They'll also eventually need local sources of supply which means a functioning local economy, which is only really possible with peace, would also be an objective. There are probably some long term complications, both good and bad. Just giving China unfettered access to middle east oil is a bit daunting, but they're going to get oil from somewhere and this way they pay a meaningful price for it.
It's a big job, but they've got a big army to do it with. If the Chinese are still leery after we've pointed out that an Iranian superpower would be a threat to them, and after we've offered them the Iraqi oil, then we push the Saudis forward with suitcases full of money and more exclusive oil contracts to bribe them into participation. Iraq may indeed be a horrible mess, but if there's one country in the world for which getting involved there might be a smart move, it's China.