Michael Totten has an interesting discussion with some Iraqis:

According to the conventional narrative, Al Qaeda was rejected by Iraqis because they murdered Iraqis. They were far more vicious and hateful than the Americans they vowed to expel. The narrative is correct, as far as it goes, but Al Qaeda is detested for more than mere thuggery. Other armed groups have been able to maintain at least some popularity even though they also murder Iraqis. None of the others, though, violent though they may be, are so thoroughly totalitarian, so alien to the traditions of Iraqi culture, and so hostile to its centuries-old social fabric. Al Qaeda in Iraq tears at Iraq