If I'm not mistaken, the big fear is that the Shia will get an autonomous state to the south, the Kurds get one to the north. All the oil money in the country is kept more under the control of each of these areas, leaving the Sunni area - which would not be an autonomous area - to suffer from a lack of funds to develop their infrastructure. Plus, this model would allow for the Shia and Kurds to make rules for the Sunni center that would be "exempt" for autonomous regions that would consist of the rest of the country.
At least, that's what I got from a few minutes of NPR this week.