The majority of the Iraqi populace is Shiite.

I think that if you discount the Kurds in the north and the Marsh Arabs/Ma'dan in the south that this is not true. I also get the impression (though I could well be wrong) that those populaces don't have any real interest in Iraqi government, and are happy to remain in their tribal structures. Based on that, I doubt that the Shiite Iraqi community would have a large impact on any new Iraqi government. Of course, this is based on my inference that those peoples would rather just be left alone, and that they don't feel that having a controlling interest in the Iraqi government would be an appropriate action.

The real solution to all of this would likely be for northern Iraq to become part of a new Kurdistan, and the southern part to become it's own Fertile Crescent nation.