That's the moderate way to go about winning a war and it's not particularily working. The BEST way to win a war is to stomp out your enemy. We never would have won WWII the way we're fighting this war. We went in and put the hammer down!
Bush's idea of moderately going about trying to win friends and influence people around extremist in countries who have no respect for human life and want to dominate the world is becoming increasingly dangerous.
And in WWII, we had a solid set of nations that we were fighting against. We fought countries and politicians in WWII.
Now, we are at war with millions of individuals, disperesed amongst many nations. “Putting the hammer down” here would have the same effect as “putting the hammer down” on jello!
Although, there is a bit to your approach that can still be used- breaking their will to fight.
Slaughter so many of their fighters in such a glorious display of might that the rest of the extremists lose their will to fight.
And in that regard, I simply say this- just watch what happens. ;)