Its the oil
The debate over the Iraqi constitution is, of course, dominated by thoughts about oil. If the Kurds keep the old vilayet of Mosul and the Shi'a have Basrah. That means almost all the oil is in those areas. This leaves Baghdad (which is Sunni and Shi'a - the city Shi'a and around Sunni) without much dosh.
One thing that amazed me about the debates about withdrawing the troops was the argument against setting a date for withdrawal (both from the Conservatives and Labour).
Their argument goes that "if we give a date for withdrawal the insurgents won't give up", the main objective of the insurgents has been to get rid of the occupation. If you give them a date upon which it ends then there is no reason for them to continue to fight (as long as that date is quite near in the future).
On the other hand if you don't give a date then they need to continue to fight.
Why anyone thinks a dispute about the constitution is going to stop the insurgency I really don't know.