Sabbahi vowed protests would go on until "we topple the constitution."
"The revolution is back ... We shall be victorious," said Sabbahi, who came in a surprisingly close third in the presidential election.
The coalition is aiming to rally together the disparate opposition factions, hoping to focus a movement that critics say failed to capitalize on its gains after Mubarak's fall. That they appear to have won a degree of acceptance among protesters is a significant shift, since mainstream liberal politicians were dismissed by many activists as out of touch, disorganized and out for their own interests.
ElBaradei's strong move to the fore is particularly notable. He was an inspiration for some of the youth in the 2011 anti-Mubarak uprising, but long appeared reluctant to play a leadership role and was criticized as remote and elitist.
The politicians still lack grassroots, warned Manal Tibe, a rights activist who was the first member of the constitutional assembly to withdraw in protest against the Islamists.
The street "is moving faster than the political opposition leaders," and some protesters worry they won't push strong enough demands, she said.
Protester Mohammed Taher, a 45-year-old computer engineer, said the rallies have been fueled by widespread outrage, not politicians' organizing. "People came here without a rallying machine," he said.
If the charter does go to a referendum, the politicians do not have the public reach or enough time to galvanize a "no" vote, she said.
The opposition also is counting on a revolt by the judiciary. Many judges have gone on strike, raising the possibility they would not serve as election monitors as required. Two top judicial bodies, the High Administrative Court and the State Council, said they would confer with the main Judges' Association on whether to monitor.
The Salvation Front warned on Friday that holding a referendum would "deal a deadly blow to the legitimacy of the president."
But if a referendum is held, the opposition faces the tough choice of whether to boycott — and risk sidelining itself — or trying to rally a "no" vote — and risk losing in the face of Islamists' powerful grassroots electoral machine.
The Brotherhood and harder-line Islamists won nearly 75 percent of the seats in last winter's parliament election. The Brotherhood's Morsi, however, won only about 25 percent in a first-round presidential vote and just over 50 percent in the runoff.
Safwat Hegazy, a hardline cleric allied to the Brotherhood, challenged the opposition in a Tweet to "go to the people in the referendum ... If the people are by your side and say no, we'll know who you are and who we are."
The opposition has been emboldened by the anger at the Brotherhood's rule after Morsi's edicts ignited criticism brewing for months that the group has used election victories to monopolize power in Egypt.
Many at Friday's protest mocked the constitutional assembly session, after watching it all night on television. During the marathon gathering, the 85 remaining members of the 100-member body voted on each of the more than 230 articles, passing all by wide margins.
The assembly's white-bearded president, Hossam al-Ghiryani, kept the voting at a rapid clip, badgering members to drop disputes and objections and move on.
At times the process appeared slap-dash, with fixes to missing phrasing and even several entirely new articles proposed, written and voted on in the wee hours of night.
In Tahrir on Friday, protesters carried signs reading, "Inside the Brotherhood kitchen, al-Ghiryani cooked the constitution."
Ahmed el-Kedwani, a spare parts shop owner, said he watched as well, adding despairingly, "These are the people who wrote the future of Egypt."
The Brotherhood " have been chasing the dream of ruling Egypt for 80 years and its only by blood that they will leave power," he said.
Associated Press writer Aya Batrawy contributed to this report.