Political leaders and the 71 members of the constitutional drafting committee on Monday went into 11th-hour talks over the charter, with still no agreement on at least two fundamental issues, federal autonomy and the role of Islam in the state.
Earlier in the day, Hussain al-Shahristani, the deputy speaker of parliament, said talks would continue until midday local time, at which point a decision would have to be taken on whether to present a draft to parliament or to look at more dramatic options.
In the afternoon, a special evening session of parliament, which was scheduled for 6pm to consider the document, was postponed for two hours.
The session which was officially set to begin at 6pm was first delayed by two hours and has now been further delayed, but no new time was given.
A few minutes before the original starting time, Tariq al-Hashimi, the general secretary of Iraq's biggest Sunni political group, the Iraqi Islamic party, told Aljazeera the disagreements were broader than simply between Sunnis and the others.
Instead, he said there still points of disagreement among Shia and Kurds and that it might be better to delay a decision.
Al-Hashimi said his party did not believe in the "sanctity" of the interim constitution which mandated Monday as the deadline for the constitution to be approved by parliament.
Kurdish parliament member Mahmoud Othman confirmed that meetings were still underway on the outstanding issues and so far "no final agreements have been reached."
Last year's interim charter, known as the TAL, laid down 15 August as the deadline for completing a draft of the new constitution, which must be voted on in an October referendum.
"The first option is that everyone agrees on a draft of the constitution and it is presented to the National Assembly for approval on time," Shahristani told reporters.
Another possibility, he said, was for the National Assembly to vote, and, if agreed by three quarters of the house, amend the TAL to allow more time to draft the new constitution.
"If they can't all agree, they will ask for an extension"
"That is a very like possibility," he said, adding that if that route were taken an extension of two weeks to one month would likely be sought.
Yonadem Kanna, a Christian member of the drafting team, also said an extension was most probable.
"If they can't all agree, they will ask for an extension," he said. "My opinion is it will be two or three weeks maximum, without the need for changing the referendum or election dates."
While that possibility exists, such a move could prove an embarrassment for Washington, which has piled pressure on Iraqi leaders to meet the self-imposed deadline. The US ambassador is playing a prominent role around the talks.
Members of the drafting committee said another possibility was that Shia and Kurds, who between them have an overwhelming majority in the Assembly and who also broadly agree on the wording of the constitution, could decide to present a draft to parliament on their own, ignoring Sunni objections.
Salah al-Mutlaq, a member of the drafting team from the Sunni Arab minority, said such a move would be unacceptable. "It wouldn't be legal, but then again not everything that happens here is legal. I think they may do it, but if they do, we will object to it in the strongest terms," he said.
One concern over such an option, besides ignoring the input of Sunnis, who dominated Iraq under Saddam Hussein and before, is that it could increase armed opposition to the government and the presence of US-led troops. One of the hoped-for benefits of an inclusive constitution-writing process was that it would sap the two-year-old revolt.
The Sunni community finds itself in a difficult situation. Since it widely boycotted elections in January, it ended up with a fraction of the seats in the National Assembly. That meant almost no representatives on the constitution-writing team, until an extra 15 seats were added.
Some Shia say Sunni members of the drafting committee are being obstructive for the sake of it, and argue that the Shia and Kurds should push ahead without them, particularly as most Sunnis are unelected members brought in last month.
"They can't hold up the drafting of the constitution just for the sake of it," said an elected Shia official who asked not to be named. "There's nothing to say that these Sunnis even properly represent their community."
Federalism and religion
One way around the looming impasse may be a fudge. Since there appears to be broad agreement on most of the text - save the crucial clauses to do with federalism and religion - it is possible that an incomplete draft could be presented to parliament and accepted in the interim.
"It's possible that we could accept a draft that covers basically 99% of the clauses and allow a bit more time to complete negotiations over the other issues," said Shahristani.
Kurdish and Sunni Iraqis have
much at stake in the process
"We could interpret the TAL in such a way as to allow that."
A spokesman for President Jalal Talabani, who has led the last-ditch negotiations, also said such a move was possible.
"The TAL says the National Assembly is to write a draft constitution by August 15. It doesn't say if August 15 has to be a final draft," said Kameran Qaradaghi. "There could be a few days to discuss some of these things further.
"It's a possibility. It remains to be legally justified."
Kurds are anxious that any wording on federalism is strong enough to guarantee their existing de facto autonomy, while Sunnis are particularly concerned to resist claims for a Shia region that could challenge Baghdad's control of southern oil.
It is uncertain that a few more days of negotiation would be enough to resolve the differences of opinion.