"We are still holding discussions on four points but the draft will be finished," Saad Jawad Qindeel, a Shia member of the committee, said.
Iraqi President Jalal Talabani, who has brought Iraqi leaders together this week in a bid to meet an 15 August deadline for presenting the charter to parliament, had earlier expressed optimism the document would be finished by Sunday.
But members of the panel sent mixed signals.
The Iraqi government and its US backers hope the constitution will set Iraq on a political path that takes the sting out of the violence in the country and allows Washington to bring many if not all of its troops home.
Saleh Mutlaq, a Sunni member of the committee, was confident of a deal on Sunday but said decisions on some thorny issues were likely to be postponed.
Under intense pressure from the United States, Iraqi politicians have been racing to tackle sticking points that cross sectarian and ethnic lines.
Though US and Iraqi officials are likely to describe finishing the charter on time as a victory for democracy, some lawmakers say postponing sensitive issues could backfire.
"If God is willing, tomorrow it will be ready," Talabani told a news conference in Baghdad on Saturday, although he said two major issues remained under negotiation.
"If God is willing, tomorrow it will be ready"
"There are no obstacles but discussions on federalism in the south and the relation between religion and state."
Anti-US hardliners have warned Iraqis not to take part in politics and they show no signs of softening their position. One committee member and an adviser to the panel were shot dead in Baghdad last month.
An Islamic hardline group issued a statement on the internet on Saturday threatening to kill any Sunni imam who voiced or encouraged support for the constitution.
Talabani's spokesman Kamran Qaradaghi hinted later the talks were heading towards accepting a softer federalism that still gave Kurds autonomy guarantees and powers to the provinces.
Bush cited the Iraq constitution
in his weekly address
"There is an opinion favouring decentralisation, with wide powers for the provinces and an assurance of the special nature of the Kurdish region," he said in a statement.
Qaradaghi said Kurdish and Shia politicians would continue talking late into Saturday night.
US President George Bush cited the constitution in his weekly radio address, describing it as a "critical step on the path to Iraqi self-reliance". He said Iraq's violence would not cause US troops to withdraw prematurely.
Some drafters in the 71-member committee have suggested postponing discussion of the most contentious issues in order to make the self-imposed deadline, but Talabani said that would not happen.
After a referendum on the constitution in October, a new general election is scheduled for December.
It is unclear what will happen if the deadline, set down in an interim basic law agreed last year, is missed.