Shibley Telhami says that his polling indicates: Arabs want a combination of many things that Turkey’s model offered: a country that balances democracy and culture, but also a stable, strong, prosperous nation, and one that makes them feel proud on the world stage. Erdogan, who personally symbolized the mix of Islam and democracy in many Arab minds — at least until the recent upheavals in Turkey — was not selected by Arabs as the favorite leader until he was seen as standing up to Israel on the 2008-09 Gaza war.

Overall, the resonance of political Islam in the Arab world — and in Egypt in particular — has been exaggerated. To win the presidency last year, the Muslim Brotherhood could rely on its political machinery and the disarray of its opponents; it didn’t need to win the hearts of most Egyptians. But as Morsi learned too late, it couldn’t govern without broader public support.

However, if Morsi and the Muslim Brotherhood overestimated the Islamists’ appeal, Egypt’s transitional rulers seem ready to dismiss it too easily. Public rejection of the Brotherhood does not translate into an embrace of the generals. Gen. Abdel Fatah al-Sissi’s popularity could be fleeting: Despite the Egyptian public’s long-held admiration of the military as an institution, especially immediately after the revolution, their opinion of the generals changed within months, with only 18 percent of Egyptians polled saying they had advanced the goals of the revolution by May 2012.

It is too early to measure the impact of the bloodshed on the generals’ public support, but the coalition around them has conflicting aims and values, even if they were united against Morsi — and it is beginning to fracture, most notably with the departure of Vice President Mohamed ElBaradei.

It was easy enough to use public disenchantment with Morsi and the muscle of the military to gain power. But in an era of heightened expectations and free-flowing information, a Mubarak-style regime cannot return. It is now impossible to govern Egypt by repressing the Brotherhood and its supporters, who have become indispensable parts of an empowered citizenry.

The bloody path chosen this past week takes Egypt into the unknown. What we do know is that all Egyptians are prepared to pay a price to have their voices heard. If that can no longer happen peacefully, Egypt must brace itself for the violent radicalization that makes democracy impossible.