If the rebuilding of Iraq is a success, one of the biggest fruits of that victory will be 26 million Arabic speakers who suddenly have the freedom to say whatever they want and the means to do so. Yes, some of those Arabic speakers will oppose the US, will even hate the US and preach violence against it. But a great many will also have a positive view of the US, and given the means to share their views with the rest of the Arabic world, this will result in a huge net increase in the amount of pro-Americanism the rest of the Arab world is exposed to.
Another major problem the US has is its lack of ability to gather human intelligence. This is something else a free Iraq will help solve, as a number of Iraqis will be willing to work with the US in intelligence gathering in the rest of the Arab world.
These two factors are far more important than they sound: The role of propaganda in anti-Americanism is vastly underestimated. Propaganda has been far more important than any US policy in creating and sustaining anti-Americanism in the world.
In a coincidentally related post, Dr. Demarche discusses how we can deny Al Qaeda its next generation of jihadis.