Daniel Pipes discusses CAIR's "Not in the Name of Islam" petition, calling it "CAIR's Phony Petition":

The petition indeed won CAIR a fistful of kudos. Among others, the Associated Press, United Press International, Religion News Service, Washington Post , and Philadelphia Inquirer wrote admiringly of it. I found not a single skeptical word on the topic.

But a close look finds this petition lacking in several ways...

...In conclusion, "Not in the Name of Islam" seeks to clean up Islam's image without doing anything of substance. It manages to do two things at once: impress naive Westerners without upsetting anyone in Hamas, Al-Qaeda, the Iraqi Islamist organizations, or other violent groups.

In this, the petition initiative fits CAIR's well-established pattern of obfuscation and insincerity.

I made similar points here.