There is a Catch 22: The Hadith prophesies that the Dajjal will conquer some people with military might, and others by benevolent seduction. Those who follow the Dajjal prosper: abundant crops, good health, long life, material comfort, etc.
Because the US is big and powerful, just about anything we do can be labeled Dajjalic by the fanatics.
But for the ordinary guy in the street, this strategy should work. Economic growth, education programs, medical and nutritional assistance should win them over, and shrink the pool from which the fanatics can recruit.
But it is important that the US be consciously AWARE of this "Dajjal" propaganda while we are doing our good works, or else it can all come to nought.
Again with the parallel with Bin Laden etc. They claim to help the people. They threaten those who don't go along with them. They not only threaten them, they kill them. Those who go along with them, they reward.