It's difficult to follow the drafting of the Iraqi Constitution (the deadline is midnight) but it looks like there are arguments over women's rights and whether Islam will be the official religon (we fought the war for that?).
But this looks like a troublesome road: The proposed draft need only be approved by a majority of their National Assembly before it can go to the voters. Simple enough. However, it would then go to the voters on a referendum by October 15.
If any three of Iraq's 18 provinces reject the referendum by two-thirds or more, the constitution will be rejected.