Over the past week, there have been reports of both continuing crisis and signs of some breakthroughs.
One of the toughest issues remains what role Islam will play in defining the new Iraq state.
Iraqi religious parties have continued to view the constitution-drafting process as their chance to press for a political system with Islamic colorings.
But they are opposed by secular politicians, including the Kurdish bloc in the National Assembly. The assembly must approve the draft charter before it goes to a national referendum due in mid-October.
Mahmud Othman, an independent Kurdish politician on the drafting committee, told RFE/RL earlier this month that the disagreements have even extended to what name to give post-Saddam Iraq.
"We don't agree to give the name of, let's say, 'Islamic Iraqi Republic,' because that gives a hint that it looks like Iran, and, you know, we will have more trouble than [it's worth]," Othman said. "Already people accuse us of being under Iranian influence."
But the most high-profile disputes have centered on religious parties' demands that the constitution designate Islamic law as the main source of Iraq's legal code.
That initiative is again opposed by secular politicians who insist that Islamic law be one source among others, including Western systems.
Resolving the dispute is critical for working out future procedural questions -- such as whether clerics who are experts in religious law will be included on the Supreme Court.
The resolution also will determine how much authority clerics will have in settling family disputes like divorce and inheritance.
That question is particularly sensitive for secular Iraqi women, who fear Islamic judges would roll back the rights they now enjoy under existing Iraqi law.
The second major issue bedeviling the constitutional committee has been how to define Iraq as a federal state.
The committee had originally expected only to have to wrestle with Kurdish demands to maintain their present high level of autonomy as part of a new federal system.
But a leading Shi'a religious party's demand to also extend autonomy to Iraq's Shi'a-majority areas has now turned federalism into a much broader and contentious issue than before.
Sunni political leaders have strongly rejected Shi'a autonomy, saying that it -- combined with the likely acceptance of Kurdish autonomy -- could impoverish the central Sunni areas.
The Sunnis worry that Kurdish and Shi'a autonomous administrations might try to hoard Iraq's oil wealth, which is in the south and north of the country.
As some other politicians from Shi'a religious parties and secular Shi'a leaders have also warned that widespread Shi'a autonomy could divide Iraq, emotions over federalism have risen.
A major question this week has been whether the committee could find some definition that satisfies all sides.
Iraqi National Security Adviser Muwaffaq al-Rubay'i, a prominent Shi'a politician, urged decentralization as a solution in an interview with Reuters on 19 August.
"I'm supporting the most decentralized system, the most federal system. I'm supporting the rights of people to self-determination, because I think this is one of the very basic human rights," al-Rubay'i said. "I'm supporting [the idea] that the local people should enjoy some of the wealth they are sitting on."
A decentralized system would give strong local powers to Shi'a regions but stop short of full autonomy.
But it still is not clear whether the Shi'a politicians have been able to find a compromise over the self-rule question either among themselves or with the Sunnis.
Yesterday, Sunni leaders complained of being largely excluded from the federalism negotiations during the past week amid charges by Shi'a and Kurdish leaders that they are being too inflexible.
Fifteen Sunni leaders said in a joint statement that "there is still no active and serious constitution so far." They added, "This constitution needs to be written by consensus, not simply a majority vote."
Iraqi officials say that if the constitutional committee is unable to produce a finished draft by today's midnight deadline, one of two things could happen.
Government spokesman Laith Kubba yesterday said the options would be to grant still another extension to the committee, or for the current interim government to be dissolved.
For RFE/RL's full coverage of developments in Iraq, see "The New Iraq"