For weeks, liberal, secular and Christian members, already a minority on the 100-member panel, have been withdrawing to protest what they call the Islamists' hijacking of the process.
The sudden rush to finish came as the latest twist in a week-long crisis pitting Morsi and his Islamist supporters against a mostly secular and liberal opposition and the powerful judiciary. Voting had not been expected for another two months. But the assembly abruptly moved it up in order to pass the draft before Egypt's Supreme Constitutional Court rules on Sunday on whether to dissolve the panel.
To come into effect, the draft must be passed in a nationwide referendum, which Morsi said Thursday will be held "very soon."
"I am saddened to see this come out while Egypt is so divided," Egypt's top reform leader, Nobel Peace laureate Mohamed ElBaradei said, speaking on private Al-Nahar TV. But he predicted the document would not last long. "It will be part of political folklore and will go to the garbage bin of history."
A new opposition bloc led by ElBaradei and other liberals said the assembly had lost its legitimacy.
"It is trying to impose a constitution monopolized by one trend and is the furthest from national consensus, produced in a farcical way," the National Salvation Front said in a statement, read by Waheed Abdel-Meguid, one of the assembly members who withdrew.
Thursday's vote escalates the already bruising confrontation sparked last week when Morsi gave himself near absolute powers by neutralizing the judiciary, the last branch of the state not in his hands. Morsi banned the courts from dissolving the constitutional assembly or the upper house of parliament and from reviewing his own decisions.
Speaking in an interview on state TV aired late Thursday, Morsi defended his edicts, saying they were a necessary "delicate surgery" needed to get Egypt through a transitional period and end instability he blamed on the lack of a constitution.
"The most important thing of this period is that we finish the constitution, so that we have a parliament under the constitution, elected properly, an independent judiciary, and a president who executes the law," Morsi said.
In a sign of the divisions, protesters camped out in Cairo's Tahrir Square who were watching the interview chanted against Morsi and raised their shoes in the air in contempt.
The president's edict sparked a powerful backlash in one of the worst bouts of turmoil since last year's ouster of autocrat Hosni Mubarak. At least 200,000 people protested in Cairo's Tahrir square earlier this week demanding he rescind the edicts.
Street clashes have already erupted between the two camps the past week, leaving at least two people dead and hundreds wounded. And more violence is possible.
The opposition plans another large protest for Friday, and the Brotherhood has called a similar massive rally for the following day, though they decided to move it from Tahrir to avoid frictions. Bands of youths have been daily battling police on a road leading off the square and close to the U.S. Embassy.
At least three independent daily newspapers are threatening not to issue editions on Tuesday in protest against Morsi's edicts and the rushed constitutional vote, according to the National Committee for the Defense of Freedom of Express, which called for the move.
The Constitutional Court's announcement that it would rule on the legitimacy of the assembly was a direct defiance of Morsi's edicts. It will also rule Sunday on whether to dissolve the upper house of parliament, which is overwhelmingly held by Islamists. Most of the nation's judges are on indefinite strike to protest the edicts.
It is not clear what would happen to the approved draft if the court dissolves the assembly. The crisis could move out of the realm of legal questions and even more into the more volatile street, to be decided by which side can bring the most support.
The opposition is considering whether to call for a boycott of any referendum on the constitution or to try to rally a "no" vote, said Hamdeen Sabahi, a National Salvation Front leader who ran in this year's presidential race and came in a surprisingly strong third.
"The people should not be made to choose between a dictatorial declaration or a constitution that doesn't represent all the people," he told independent ONTV, referring to Morsi's decrees. "He is pushing Egypt to more division and confronation."
During Thursday's session, assembly head Hossam al-Ghiryani doggedly pushed the members to finish. When one article received 16 objections, he pointed out that would require postponing the vote 48 hours under the body's rules. "Now I'm taking the vote again," he said, and all but four members dropped their objections.
"We will teach this constitution to our sons," al-Ghiryani told the gathering.
Islamist members of the panel defended the fast tracking. Hussein Ibrahim of the Brotherhood said the draft reflected thousands of hours of debate over the past six months, including input from liberals before they withdrew.
"People want the constitution because they want stability. Go to villages, to poorer areas, people want stability," he said.
Over the past week, about 30 members have pulled out of the assembly. As Thursday's session began, the assembly held a vote to formally remove 11 of those who withdrew and replace them with reserve members who largely belong to the Islamist camp.
As a result, every article passed overwhelmingly. The draft largely reflects the conservative vision of the Islamists, with articles that rights activists, liberals and others fear will lead to restrictions on the rights of women and minorities and on civil liberties in general.
One article that passed underlined that the state will protect "the true nature of the Egyptian family ... and promote its morals and values," phrasing that suggests the state could prevent anything deemed to undermine the family.
The draft says citizens are equal under the law but an article specifically establishing women's equality was dropped because of disputes over the phrasing.
As in past constitutions, the new draft says that the "principles of Islamic law" will be the basis of law.
But a new article states that Egypt's most respected Islamic institution, Al-Azhar, must be consulted on any matters related to Shariah, a measure critics fear will lead to oversight of legislation by clerics.
Another one seeks to define "principles" of Islamic law by pointing to particular theological doctrines. The term "principles" had long been intentionally vague, allowing wide leeway, and specifying its bases could give Islamists leverage to implement and expand the reach of Shariah.
The draft also includes bans on "insulting or defaming all prophets and messengers" or even "insulting humans" broad language that analysts warned could be used to crack down on many forms of speech.
The committee has been plagued by controversy from the start. It was created by the first parliament elected after Mubarak's ouster. But a first permutation of the assembly, also Islamist-dominated, was disbanded by the courts. A new one was created just before the lower house of parliament, also Brotherhood-led, was dissolved by the judiciary in June.