This is what cannot be done, and the very possibility of a new central state is precisely what has set off the bloodshed. It is not the case that the groups in Iraq cannot get along. What they cannot do is get along under a central state ruled by some other group. This is the basis of the bloodshed.
So what should happen? The US should abandon Baghdad. It should, in effect, allow the country to "fall apart" in the same way that Gorbachev let his empire dissolve. Iraq would split into many states, some of them noncontiguous. Governing units of all shapes and sizes would appear. The main reason for the ghastly killing – fear of the rule by one group over another – would vanish. Here is the highest hope for peace in Iraq.
So long as the US insists that Iraq be a single nation under one government, it will inspire chaos and killing. Bush was wrong, but in a way that is usually not understood. His mistake was not in overthrowing the state but in hoping to create and control a new one.
I don't think abandoning Baghdad is the answer, but I do think letting the people of Iraq split up the country as they see fit is.