Gehad El-Haddad, senior adviser to the Muslim Brotherhood, said the constitution, while vague in some places, largely received strong support in the assembly.
"At the end of the day, this constitution has a fairly strong representation of the Egyptian society," he told CNN.
Some critics argue the constitution could move Egypt closer to Sharia law. Mohamed Naeem, a member of the Eyptian Social Democratic Party, said it opens the way for a theocracy.
A 1971 constitution in place under Mubarak was "more open and protective of individual rights," said Mustapha Kamel Sayed, a professor of political science at Cairo University.
The preamble includes language pertaining to women, stating that they are equal to men but also accentuating their role as mothers.
The constitution says: "There is no dignity for a nation which does not honor women; women and men are equal, for they are the fort of motherhood, half of the society and partners in all the gains and national responsibilities."
Citing the family as "the foundation of society," the document guarantees free maternal health care and promises to reconcile "a woman's duties toward her family" and her job.
But Heba Morayef, the Egypt director for Human Rights Watch, argued that the language regarding women is too vague. She worries that the mention of women's family role will trump other freedoms.
The United Nations' high commissioner for human rights, Navi Pillay, urged Morsy to reconsider the draft, saying a number of measures contained in it are incompatible with international human rights law. She called them "not yet sufficient."
Many people in Egypt doubt the draft will bring them the freedoms they fought so hard for last year.
Tens of thousands of protesters Friday packed Tahrir Square, the epicenter of 2011's revolution. They prayed and listened to a cleric call Morsy a "pharaoh." Women in the crowd spoke of their concerns.
Businesswoman Faten Khalil said people don't trust the government and want Morsy to step down.
"They use religion to push us to do whatever they want but they are not really religious," she said.
Another Tahrir protester, designer Basna Azmi, criticized the Muslim Brotherhood, saying it is more an international organization than an Egyptian one.
Demonstrations have become violent at times, and protesters pitched a tent city at a traffic roundabout. Food vendors have set up stands in the middle of the street and protest leaders have walked across a sound stage leading chants.
Opposition factions have called for another mass demonstration in Tahrir Square starting near daybreak Saturday.
The Muslim Brotherhood has called for its own demonstration outside Cairo University on Saturday, in what would be the biggest public show of support for Morsy.