While many Sunni Arabs still support al Qaeda, a growing number of key tribes and families do not. Worse yet, for the terrorists, Sunni Arab tribes, clans and families are increasingly at war with al Qaeda. Sunni Arabs are killing al Qaeda groups they believe were responsible for the death of family or friends. But it's also about money, and war crimes trials.
The government controls the oil, and the oil revenue is given out in the form of jobs, bribes and all manner of good things. The coalition also controls billions in foreign aid. This also gets disbursed in the form of jobs and purchases. The coalition also has very effective soldiers that make sure the Sunni Arabs don't cheat when they take money. No longer can Sunni Arabs join the police, and still work with the terrorists. If you want to be a cop, you have to act like one.
The Sunni Arabs never expected all this armed resistance, to Shia and Kurdish rule, to get Sunnis back in power. What they want is a deal on the question of war crimes trials and revenge in general for their complicity in Saddam's decades of atrocities. The armed resistance gives the Sunni Arabs something to bargain with. Of course, the major members of Saddam's gang will go to trial, but there are thousands of lesser officials, nearly all of them Sunni Arabs, who also have blood on their hands, and real concerns about prosecution (legal, or otherwise.) Negotiations have been intense, and many of the Sunni Arab clans and families involved have begun to actively battle al Qaeda gangs in their neighborhoods. These groups are a mixture of Iraqis and foreigners, and are basically armed religious fanatics. There's no negotiating with them, and the terrorists don't apologize if one of their suicide bombers accidentally kills a lot of Sunni Arab civilians. It's Gods will, and all that. Increasingly, Sunni Arabs are fed up with this, and killing al Qaeda in their vicinity, or driving the fanatics out. It will be difficult to prosecute a lot of lesser war criminals who have recently become heroes by fighting al Qaeda.
Al Qaeda members won't negotiate with the Sunni Arabs over compromising with the new Iraqi government. According to al Qaeda belief, the new Iraqi government is illegitimate. The government is the creature of a democratic vote, which al Qaeda considers un-Islamic. Only God can decide such things, not the votes of the people. Moreover, this illegitimate government also allows foreign, non-Moslem, troops to stay in Iraq.
Given a choice between a job with the police or government, and more terrorist violence, the majority of Sunni Arabs are going with peace and paychecks. Each household is allowed to have one weapon, usually an AK-47. The government tolerates, for the moment, clan and tribal chiefs maintaining personal security forces, which sometimes amount to hundreds of armed men. As long as the al Qaeda and anti-government fighters continue to be turned in, dead or alive, the government tolerates the private guns. Al Qaeda is being driven out of the country, and the most effective weapon is not a gun, but angry stares and muttered threats.