That raises the question that is causing acute tensions in Cairo: If the Muslim Brothers - and their offshoot, the Freedom and Justice Party - don't want the Turkish model, what do they want? An Islamic state (even though they deny this)?
Why did Erdogan's advocacy of the Turkish model make them so mad?
These questions are being debated all over Cairo, as Egyptians prepare for the Eid al-Adha feast, after which they will begin to vote in their first free elections that begin Nov. 28. Many liberal and leftist Egyptians are deeply frightened. If the Brotherhood aces the elections, they believe, it will move slowly but surely toward the Islamicization of the Egyptian state.
"They will pretend to be open-minded until they take power," I was told by Naguib Saweris, a business tycoon and Coptic Christian who leads and finances the most prominent liberal party, the Free Egyptians. Sitting in his office atop his family's high-rise business tower overlooking the Nile, he said tensely: "What happened in Iran will happen here."
Such fears have made many (though not all) Egyptian liberals enamored of the Turkish model, in which a strong military provided a bulwark against Islamists until they eventually modified their program.
The Egyptian military, too, is no doubt enamored of the Turkish model. The generals, who were initially comfortable with the Islamists, are getting nervous that they might do too well in the elections. So the Supreme Military Council, which is temporarily ruling Egypt, has been promoting a set of extra-constitutional "principles" that would guarantee the military's power and perks. These principles would also limit parliament's role in choosing a committee to write the new constitution, thus curbing the Brotherhood's strength.
This military aspect of the Turkish model is one major reason the Brotherhood rejects it, as Essam el-Arian, vice president of the Freedom and Justice Party, told me.
A law and medical school graduate, Arian spent years in prison during mass arrests of Islamists and is considered among the more pragmatic Brotherhood members. I met him in the Brotherhood's cramped headquarters on Roda island facing the Nile, a far cry from the fancy new building that houses the Freedom and Justice Party.
Turkey's secular constitution, he said, gives a special role to the military, which endears the Turkish model to Egyptians "who are our [political] competition. We [the Brotherhood] don't welcome a secular constitution or a role of the military." Arian complained about the military's attempt to guarantee its power: "The rule of the military is refused except by a few intellectuals. The public is opposed."
But as he continued talking, it became clear that the Brotherhood had additional reasons for rebuffing Erdogan and was far more conservative than Islamist movements in Turkey or Tunisia.
"In the Muslim world, we have a different role for religion in accordance with our different history and cultures," he explained. "Egypt is different from Tunisia," he said, an interesting distinction since Tunisia's elections just returned more than 40 percent of the vote for the moderate Islamist party Ennadha, whose leaders back extensive rights for women and an openness to other cultures.
"What is acceptable in Tunisia is not acceptable here," he said.
Arian went on to complain that the terms secular and secularism make a bad impression in Egypt, while "in Turkey this term is welcomed."
To the Egyptian Muslim brothers, secular means "anti-Islamic." The idea that religion can be separate from politics simply cannot be digested by them.
But he rejected some of the claims I've heard most often from secular opponents. He insisted that his party "would hand over power if we lose. That is the key point of democracy: respect for other opinions and rotation of power."
He also insisted that his party had no intention of adding terminology to the constitution to make explicit demands that all legislation comply with Islamic sharia law. Article 2 of the constitution already states, loosely, that the "principal source of legislation is Islamic jurisprudence." This was a formulation liberals once had hoped to remove; now they seek only to prevent more specific sharia demands.
"We believe we can be religious and democratic," Arian insisted.
He is asking other Egyptians to take this pledge on faith. Many are not inclined to do so. They agree with Erdogan, who said that secularism "means respect to all religions" and should not be confused with hostility to religion.
It's hard to see how this gap in perceptions will be bridged.
Nor is Egypt's army able to emulate the actions of the much stronger Turkish army, which crushed radical Islamists in the 1990s. Such a crackdown in today's post-Tahrir Egypt would be out of the question.
The Turkish model may be Egypt's best hope, but it is unlikely to be replicated here.
E-mail Trudy Rubin