The Egyptian-style liberals make these calls knowing that a crackdown by the military or police against a committed, cohesive, religiously inspired opponent could lead to bloodshed. The protesters have fortified their positions with sandbags and brick walls, and their encampments are filled with women and children. They vow not to disperse until Morsi - now being detained without charges in an undisclosed location - is returned to office.
Egyptian authorities warned the media Sunday that they would be coming soon to cordon off the encampments. Rumors swept through the sit-ins that security forces would arrive with the dawn Monday. But authorities have apparently postponed any action.
Foreign Minister Nabil Fahmy told the BBC on Monday that the government has spent three weeks trying to reach an agreement with the protesters, but that a court order to oust the Morsi supporters is also being sought. "This is a parallel track process, and ultimately it has to be resolved very soon, either by dialogue or the rule of law," he said.
"There are conflicting positions inside the government, and even inside the security forces, about the best course of action," said Karim Medhat Ennarah of the Egyptian Institute for Personal Rights.
"These sit-ins are massive, and even if the government decides to do go in, with brute force, without respect for human rights, they would face a lot of casualties - on both sides," Ennarah said.
Yet if some liberal voices, such as ElBaradei, advocate for more dialogue and a go-slow approach against the sit-ins, they are being drowned out by calls for law and order made by liberals and leftists - many of the same people who decried the heavy-handed actions of Morsi and his predecessor, Hosni Mubarak.
"This is a violent and armed sit-in and it is the right of every government to disperse it by law, and the people are saying that if the government does not disperse, we will do it ourselves," said Karima el-Hifnawy, a leader of the Egyptian Socialist Party, one of the prominent groups representing the left.
The liberals and their leftist allies say the protests are not only illegal but disruptive to the life of the city, and that they represent a stubborn unwillingness to accept the new realities demanded by a popular revolution.
Moreover, they say, the sit-ins harbor Muslim Brotherhood leaders who have been charged with inciting violence and killing opponents.
"Protesters at peaceful sit-ins do not build walls and blockades. These protesters have weapons and they torture people, and the government should take the responsibility and disperse them," said Rawi Toueg, member of the Supreme Committee at the Free Egyptians Party, a liberal group.
Hani Salah el-Deen, a media advisor for the Morsi's Freedom and Justice Party, said that Egyptian liberals are hypocrites.
"Now the masks are falling and the liberals are confirming over and over that they have no principles, they have no logic and common sense," he said, "when they keep demanding that the authorities break apart the protests, knowing it could result in over 10,000 martyrs."
Many liberals fought alongside the Muslim Brotherhood and other Islamists to oust Mubarak and to limit the power of the military after he was gone. Many liberals here also voted for Morsi in the final round of the presidential election, after their preferred candidates failed in the first round.
Now many liberals call the Muslim Brotherhood a traitorous and terrorist organization, and say its leadership should be barred from participating in politics, similar to their demand to ban Mubarak's political party after his fall. The liberals allege the Brotherhood is theocratic to its core and guilty of inciting sectarian violence.
"In peaceful protests, yes, there may be some human rights violations, but with the Muslim Brothers, there are always guns. We're sure they are armed. These sit-ins should be dismantled, by any means, and unfortunately, there will be injuries and probably deaths," said Shadi Ghazali Harb, a London-trained surgeon and founder of the liberal Awareness Party.
"Liberals see the Muslim Brotherhood as a fundamental threat to all they hold dear, and that takes precedent above all else," said Shadi Hamid, director of research for the Brookings Doha Center.
"This hatred of the Muslim Brotherhood by many liberals has become so visceral it is hard to understand from the outside. It is so intense that they would support a forced dispersal of the protests, even if it involves the killing of unarmed civilians," Hamid said.
"Perhaps we in the West were confused by the word 'liberal,' which we associate with a tolerant and dispassionate attitude towards difference," wrote James Traub, a fellow of the Center on International Cooperation, in Foreign Policy magazine. "When the stakes feel truly dire, as they do in Egypt, liberalism itself can become a form of zealotry."