The Republicans seem to have a hard time reading the room on the torture issue, so I'll try to make this really simple. Democratic society requires an open government - those in power tell the public what they're doing, and voters see what they do, evaluate the results, and return their elected representatives to power, or not. The one exception is national security, where the government can't always tell us everything that they're doing without endangering the original mission of defending the country. So for these policy issues, and to a limited degree, the government gets to say "Trust us on this one; we're working in your best interest," and the public lets them continue their work behind a certain veil of secrecy.
The other side of this coin, of course, is that government actors working on national security have an extra obligation to act in the public's behalf and not, say, for personal or partisan gain. And here, pure and simple, is where the Republicans abused the nation's trust, exposing themselves as a bunch of amateur-hour Bernie Madoffs ("amateur-hour" because they didn't get away with it for nearly as long, and because after all their huffing and puffing about advanced, sophisticated interrogation techniques, it turns out they were no better than the small-town sheriff who tells his deputies "I need a conviction here, so if the suspect hasn't confessed yet, keep beating him until he does.")
This is what Dante reserved his ninth circle of hell for - the combination of selfishness, ruthlessness, and sense of entitlement that leads someone to take advantage of the trust bestowed on them by their fellow citizens. It's the same reason people are mad at Wall Street - we accepted their huge salaries and trusted them to make our markets work, then found out they were only in it for themselves. Time after time, Republicans abused power, hid what they were doing, then lied to us about it, all in the putative cause of keeping us safe, but really, it turns out, to save their own skins. (Those of us living in New York are especially sick of former administration officials going on about how they saved our city from attacks after 9/11 - we remember only too well the jacking up of the terror threat levels during the 2004 campaign whenever things seemed to be going badly for Republicans, and the "major plots" they uncovered that had a long way to go before they could be deemed "half-baked.")
The Republicans exhausted our patience long ago. That's why no one believes them when they say that torturing suspects uncovered and foiled actual plots - I give this much less than a 5% chance of being true. So when Dick (aptly named) Cheney goes on TV yet again, braying on yet again about how our torture program saved lives, he reveals two truths about himself, one ugly and one rather pathetic. First, he exposes himself as morally bankrupt by failing to understand that torture is just wrong and un-American, period, end of story. Second, he is too out of touch with the American public to see that outside his cloistered world of lackeys and fawning Fox flacks (I need to copyright that phrase), no one believes him or cares what he says any more. The same goes for Republicans in general, and to regain our trust they need to start by acknowledging that torture is wrong, and that there were some great wrongs committed here.