There's an arrest warrant out for Mohamed El-Beltagy, but the top Muslim Brotherhood official isn't hard to find. He's among the tens -- and at today's Friday prayers probably hundreds -- of thousands of supporters of the Islamist movement occupying the streets around the Raba'a El-Adaweyya mosque in eastern Cairo.

Egypt's security forces would have a hard time arresting Beltagy and other Brotherhood leaders wanted in connection with charges such as inciting violence so long as they are in the Raba'a area. If they tried, there would be bloodshed on a scale not yet seen. That's why when Mursi's supporters say they won't be going home soon, it's probably true. As well as protesting the removal of Egypt's first democratically elected president, they are protecting their leaders with their bodies.

There's no joy in this sit-in. The streets leading toward the mosque are blocked off by makeshift stone walls, with home-made riot shields lined up behind them in preparation for an attack. Some men in the crowd carry clubs and wear construction helmets. Cairo is hot in July -- rising to 38 degrees Celsius (100 degrees Fahrenheit) in the shade, of which there is little. And because this is Ramadan, Muslims, who make up 90 percent of the population, aren't supposed to eat or drink water between sunrise and sunset. So teams equipped with plastic jerry cans strapped to their backs walk through the throng spraying heads with water.

A temporary clinic next to the Raba'a mosque was taking in approximately 20 dehydration cases per hour, according to Ahmed El-Azazy, a general practitioner. In the 10 minutes I stood at the entrance, two people were carried in unconscious after fainting in the heat. Several others walked, or rather staggered in, and were put on intravenous drips. Azazy was on duty July 8, when the clinic handled gunshot wounds from a clash with the military up the road in which more than 50 people died.

The occupants of Raba'a say that despite the violence and harsh conditions, they have no temptation to retreat. "I brought my family 500 kilometers, from Sinai, and we will sleep here in the sand for 10 years if necessary," says Hani Fawzi, a 51-year-old math teacher. Others in the crowd raise him: "Democracy or death!" said a man in a Manchester United shirt. Friday prayers had just ended. As far as the eye could see, rows of kneeling men filled the boulevard running past the mosque. The imam ended by calling for God's protection and the return of deposed President Mohamed Mursi.

It isn't clear how this stand-off will end. If Egypt's generals were to reinstate Mursi, who is thought to be under house arrest, they would expose themselves to revenge at the hands of the Muslim Brotherhood. The huge anti-Mursi protests that triggered the coup might return. The Brotherhood's leaders, meanwhile, can't afford to leave Raba'a without returning to power. If they do, they can expect to end up in jail. So what's the group's strategy? Beltagy says there is no direct contact between the leadership and the military, but they are talking to each other through intermediaries, including foreign ambassadors. The message the Brotherhood is delivering, he says, is that if Mursi is returned to office, the upper house of Parliament is reconvened, and the constitution is restored, then the Brotherhood will agree to early presidential elections and will grant amnesty to everyone who carried out the coup.

"Compare this to their way of dealing with these issues, which is to kill people and send their opponents to prison," says Beltagy. It's hard to argue with him on that.

According to Beltagy, the military is sending back the message that Mursi's return is impossible, but if the Brotherhood backs down and its supporters go home, then the arrests and the "framing" (Beltagy's word) of people for crimes will stop.

I ask Beltagy if that might be the basis of a deal. He looks at me as though I'm dim. "If they really want to let people go, why are they arresting them?" he asks.

Most of the Muslim Brotherhood leaders spent substantial periods of their lives in jail under former President Hosni Mubarak, and prosecutors this week re-opened an investigation into how Mursi and more than 30 other Brotherhood members were freed from Sinai's Wadi Natroun prison during the 2011 uprising. Beltagy probably has a point.

He seems bitter, but not humbled. Asked if he agrees with the many analysts outside Egypt who say Mursi's removal represents a historic defeat for the Brotherhood, he answers, "If you believe this, then you are saying that history is a lie. This experiment of crushing, even annihilating the Muslim Brotherhood was tried many times before and it failed. Instead we became stronger and spread around the world."

This probably won't come as a comfort to U.S. Ambassador to Egypt Anne Patterson, but Beltagy believes she and President Barack Obama's administration played the lead role in ousting Mursi. That could be seen as an endorsement of sorts, given that Patterson has come under withering fire from critics in the U.S. and Mursi's opponents for supporting the Brotherhood and opposing this month's protest-backed coup.

"The American administration and the U.S. ambassador have been an integral part of the coup from A to Z," Beltagy says. He dismisses Patterson's warnings last month that Egyptians should stick to ballot-box democracy as a cover, designed to dupe the naïve. "All that U.S. talk about democracy, the ballot box and human rights has suddenly been thrown into the garbage," says Beltagy. "We spent years struggling to convince our people to take the democratic, non-violent path. The message the U.S. is sending now is that there is no peaceful way to transfer power in this region."

Beltagy admits that somewhere along the line, Mursi and his government lost a lot of the people who voted for them in 2011 and 2012. "One mistake that President Mursi made was a misplaced trust in the deep state. He believed in giving time for these institutions to reform," says Beltagy, and he is right. One of the main complaints of Egypt's anti-Mursi Tamarud youth movement has been that the president failed during his year in power to clean out and restructure the police, intelligence services and other hated Mubarak-era security agencies.

"Now it is clear where to start in getting the revolution back," Beltagy says. The old agencies have become more visible again since the military assumed power and doubtless have no intention of getting cleaned out. That's one more reason why finding a peaceful way out of the current deadlock is going to be tough.

(Marc Champion is Bloomberg View editorial board member. Follow him on Twitter.)