I don't think it IS "Winnable" YET<---------(Depends on if the rest of the world feels threatened enough to act in concert with us to REALLY shut down the threat).
It's a gross over-simplification on my part but essentially, the way I see it is that we've (The world/history/fate ect) "Fast-Forewarded" a culture 500 years into the future (Our present) and given them access to modern technology without the "Liberalization" that SHOULD'VE happened along the way.
The Turks sat on these people for centuries and trapped them culturally to maintain an empire. When the Ottoman empire failed the Brits and French stepped-in and carved the region up to suit THEMSELVES and post WW2 when THOSE influences receded the cold-war (And Soviet backed strong-men) stepped-up and further retarded their progress.
In the void (Of outside rulers) that exists today they've Got a hell of a problem on their hands. They've missed centuries of developement, never had their OWN industrial revolution (The Korans prohibition against interest stiffles investment), Never had a reformation of their religion (The evolution of Sharia effectively stopped after the Turks took over) and NOW, they look around at the rest of the world (Especially the west) and see "Infidels" enjoying liberties and freedoms (As well as very high standards of living comparatively) that they can only dream of at this point and it pisses them off. THEY'RE the "TRUE" followers of God's last prophet and THEY should have these things and for things to have gotten THIS screwed-up for them it MUST be the work of .........(Satan?)? It's an easy sell for the Imams and clerics who draw power from their third-world congregations. Israels just a "Side-show" (Albeit an inportant one) to these people that reinforces their view that "Something's" gone terribly wrong and needs Gods attention (With THEM as his Army).
Short of them being able to accept the idea's of democracy and tolerance (Both of which were in very short supply hundreds of years ago when their progress WAS retarded) and the benefits of them in a generation I'm not sure the world has time to wait for them to catch up (?)
Right now they're dominated by priests, kings and strong-men like the west was 600 years ago. The difference is that the Pope 600 years ago didn't have an A-Bomb up his sleeve and they just might in a couple more years. A-Bombs, long-range missiles, stagnant, totalitarian governments and 14th century mysticism existing side-by-side with 21st century, secular democracies is a bomb thats had it's fuse lit.
We just don't know how long that fuse is (?)