Cairo   Walk south along the Nile in Cairo’s febrile downtown, past austere, colonial-vintage government buildings and stately luxury hotels, cross into Tahrir Square, and you’ll pass from one authority to another. Outside, tanks and armored personnel carriers guard Egypt’s besieged and maligned government; inside the square, in the heart of the city, hundreds of thousands of protesters and revolutionaries hold jurisdiction, establishing a parallel capital where dictator Hosni Mubarak has little control. Those who for years lived in fear under Mubarak’s regime openly taunt police. Impromptu lectures and debates erupt on the curbside, near the Ministry of Information, no less. “I see the world with new eyes,” one protester told me.

The demonstrations, which started on January 25, were called by a small group of longtime activists, including the loose-knit Kefaya movement, the Revolutionary Socialists, supporters of Nobel laureate Mohamed ElBaradei, and other groups. They expanded to a size that not even the leading activists imagined possible. “On the first day, no one wanted to come because they thought it would never work,” said Amna Shawkat as she hoisted a sign cursing Mubarak. “But people started seeing how big it was. Now everyone is coming.” By its second week, the demonstrations had grown into a broad-based movement that encompassed secular liberal parties, the Muslim Brotherhood, left-wing groups and perhaps the largest contingent: unaligned first-time activists.

The government simultaneously launched a brutal crackdown and offered a number of concessions, including a pledge from Mubarak to step down in September, which most demonstrators rejected, insisting on his immediate resignation. Some leading opposition figures met with Omar Suleiman, Mubarak’s longtime intelligence chief, named vice president soon after the demonstrations erupted. Suleiman also promised concessions, but he refused to countenance the immediate resignation of Mubarak. I asked a number of protesters what they thought of such negotiations, and Mubarak’s promise. “These people talking to the government don’t represent us,” said Muhammad Sharif, a mechanical engineer, echoing a widely repeated sentiment. “No negotiations with anyone until Mubarak is gone,” said Sabr Muhammad, a cobbler, who has been living in a grotty tarpaulin tent at the square’s center for more than a week.

This highlights deeper divisions between many of the older, established opposition parties and activists on the ground. In fact, most protesters insist that they want not only Mubarak’s departure but also a thoroughgoing overthrow of the entire system he has established, including the dissolution of a Parliament many see as rigged and the ouster of all officials from the ruling National Democratic Party. But some of the opposition parties have been equivocal. One leading figure of the Muslim Brotherhood, which wields the most influence of any party, said in a press conference, “It’s safer that the president stay” until the Constitution is amended to limit his powers. But shortly afterward, another leading Brotherhood figure insisted on Al Jazeera that there would be no talks without Mubarak’s resignation.

The unabating size and fervor of the protests, which have taken hold in a number of cities across the country, have prevented the established opposition groups from veering too far from popular demands. “The Brotherhood and the secular liberal groups are under tremendous pressure from the youths” on the ground, said one opposition leader, who declined to be named.

Government attempts to drive a wedge between the formal opposition and the masses in the streets are not the only challenge. An unremitting government campaign to highlight the chaos, the drop in tourism and claims of hidden “foreign hands” has blunted the enthusiasm of some supporters. “This is not good for Egypt,” said Abdul Hassan, a driver, who told me he had originally backed the protests. “We need a normal life.” Some of the popular committees—autonomous neighborhood watch groups that appeared after the government removed the police from the streets—have turned against the protests, citing state television allegations of foreign agents stoking the unrest.

But protesters are countering state propaganda by persuading friends and family to join the demonstrations—with much success. Indeed, the crowd at Tahrir Square on February 8 was likely the largest so far, with people spilling over into the side streets and thousands of workers striking in solidarity. On that day I watched as a young girl took the stage and, to riotous applause, sang a song mocking Mubarak’s wife, Suzanne—an unthinkable act mere weeks ago. Mubarak himself was hung in effigy, the dummy’s limbs pinioned and the torso twirling lazily in the wind. Some protesters slept beside graffiti-daubed army tanks, while others carried signs imploring the United States to cut ties with the Mubarak regime and leave Egypt alone.

Out of the seemingly formless mass in the square, some semblance of organization has arisen. Committees take care of logistics—to direct supplies of food and water as well as take care of sanitation; awareness—to counter government claims and spread word of new protests; security—to check for police agents and weapons; and other issues. Demonstrators have even mooted the idea of holding elections to establish a formal leadership. Many have rallied behind figures like Wael Ghonim, a 30-year-old marketing executive for Google whose Facebook page protesting police brutality was instrumental in starting the protests. He was detained by the government for twelve days, and upon his release gave a riveting TV interview that invigorated the demonstrations.

Intense debates over Egypt’s future take place on the sidewalks, in tents, on the barricades. There are a dizzying number of opinions, but all sides in Tahrir Square are in agreement on one thing: “Mubarak has to go. Anyone who claims otherwise doesn’t represent us,” said Ahmed Maher, a founder and leader of the April 6 Youth Movement, which originated three years ago in solidarity with labor struggles and played a leading role in organizing the January 25 protests. “We’ll need patience, but we’ll wait until we get what we want.”

At the close of the second week of protests, with hundreds of tents arrayed throughout the square and standing-room-only crowds, it looked like the protesters might do just that.