I think their organization can be erased with a mixture of fighting fire with fire and removing the fuel source.
Radicals who are going to blow themselves up are already over the edge for the most part. The only way we're getting rid of them is to be stronger than they are when they attack. As the safety situation improves in Iraq (and anywhere in the world), as fathers are working stable jobs, and mothers don't have to worry about the kids being safe when they play, when children are in school and learning how to be successful, terrorism and extremism will die.
The argument that you can never get rid of them all is certainly true, as evidenced by certain members of our own societies. But when they're down to such small numbers, it becomes a police issue.
Life in Iraq is moving back towards normalcy. The people are remembering what it's like to live in safety in a first world nation. As this realization sinks in, they're turning on the bad guys, and finally progress is being made.
If we choose to simply not believe any good news that comes out of country, that is our prerogative. I think looking at it historically though, the media is far more interested in putting bad news on the telly than good.
