i think the only way to defeat it is to allow a counter active group by more middle of the road muslims....
I think to defeat it, you have to look at it as not a problem solvable by military means alone. There are multiple causes - political instability, income inequality, corruption, social unrest, lack of education, lack of opportunities that can lead to increased radicalization. When a state is failing, or can not provide for or protect it's people then they turn to tribal, ethnic or religious indentificaiton rather than national to survive. Religious furvor increases in bad times, it's easy for extremists to make the case that outside devils are the cause of all these problems and unite people behind them because the state can't do that. That's why a big part of any solution must come from the Muslim communities and especially those countries but it isn't easy.
I was listening to NPR while driving home from work last night and
they had a story about Egypt, and it's population crisis. I didn't realize Egypt was the most populous country in the Middle East. It's economy is a wreck and it's has an abysmally low rate of literacy. In fact the economy was one of the driving factors in the ouster of Mubarrek. Without education, with out the means to cllimb out of poverty and improve your situation - how can you fight extremism that makes so many promises that if you will be a "good Muslim" (according to their definition) - everything will get better?