Is the war against terrorism winnable?

Yes... But It Requires Commitment And The Eradication Of The Problem...
But Congress Will not allow it... They Have No testicular Fortitude and Very Little Spinal Fortitude...

About as winnable as the War on Drugs, therefore the answer would be no. There will always be terrorists, and as such there will always be terrorist attacks and as long as there are terrorist attacks then we'll always be at war. There is absolutely no way in the world to appease everyone, either politically or religiously, which are the two main reasons for terrorism.

Well, that depends. What does winning look like to you?