From a conversation with a left-wing German colleague at work:
The Americans aren't going to solve the Shia-Sunni conflict. I don't think they need to. The key is to change the methods by which the battle is fought.
There was a classic European author (I can't remember who) who said that the reason there was religious peace in Amsterdam had nothing to do with a lack of desire of individual groups to control and direct others. It had to do with the fact that there was a multiplicity of groups - none of whom had the power to dominate. Peace was not through the elimination of faction, but through the multiplication of it. Faction is multiplying in Iraq. There are quite a few parties, the Shia aren't all aligned with each other and neither are the Sunni. Before long, the locals will realize there's no purpose to the fight. This is why the Sunni tribesmen have turned against Al-Qaeda and the other militants in a big way. The fight is being sustained, not by Iraqis, but by foreign fighters - foreign fighters who have no problem killing lots of civilians just to maintain chaos. This was the strategy laid down by Zarqawi before he was killed - his correspondance calling for it was clear. Iran is doing the same thing. If these guys can be slowed down (and I think they can, once civilians can see that America isn't withdrawing and they and their families won't be killed if they resist), then the country will settle into being a very contentious, somewhat liberal, democratic state.
The American role isn't to bring peace to both sides. It is to provide the support necessary to allow a political/religious marketplace to develop. It is like the accumulation of wealth. You can get wealth by stealing it or forcing others to give it to you (the main method for a long time) or you can get wealth by creating value. The market serves as a mechanism to enable the latter approach at the expense of the earlier one. The Americans can provide the conditions, by fighting extremist groups, for this sort of political market to emerge. If this sort of political marketplace can emerge ANYWHERE in the Arab world, it will be tremendously positive for all of us. The example can be greatly helpful to all Arab peoples living under the twin impositions of totalitarian dictatorship or the potential rise of the Muslim Brotherhood. The Arab world trails even Africa in terms of education, for example. There are real problems, but they don't need to be that bad. The Arab world can be a much more pleasent place - and it has been. Muslim countries can succeed in having this sort of marketplace. For all it's problems, Turkey isn't such a bad place. If they had nukes, I wouldn't care. Iran can also have this sort of marketplace - and under liberal leadership I wouldn't care whether they had nukes. Lebanon wasn't too bad prior to the civil war - it was long-term flaws in their constitution that brought them down.
If there can be a marketplace of ideas within the Arab world, the export of a tremendously destructive vision can be brought to an end.