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A substantial percentage of the public is never going to believe that refraining from the use of torture is more effective than torture in preventing terrorist violence.
I think this is largely true, but I think there's also an overpowering emotional element involved as well. To many Americans, particularly since 9-11, the idea of the "good guys" torturing a "bad guy" (begging the question of whether he is actually a bad guy) is emotionally satisfying, while the notion that such a vicariously cathartic activity might be stopped or impeded by canniving civil libertarians is at least as emotionally repellent.
"24" itself depicted this dichotomy, with an insidious efficiency. I remember one episode from one of the first seasons in which a detainee was going to be tortured for vital intel, and a walking stereotype from the ACLU (or something) showed up with a court order (damn activist judges!) to stop it at the most dire moment. I think Jack Bauer knocked him out or something, and the inevitable consequence was that his efforts were rewarded with helpful information.
That's why the fictional, fantasy realm of "24" is so important to understanding the emotional component of so many Americans' support for torture. As much as supporters of torture insist that it's not "punishment," for millions of others it certainly is, and that's why they like it.
Just for kicks, here's a little thing I wrote lampooning "24" and conservatives' crazed lust for timers and emergency scenarios (also at signature): http://insideoutthebeltway.blogspot.com/2008/05/jack-bauer-fisa-reprised.html