Democrats have generally been opposed to torture. That's half the country right there. For the other half of the country, a huge part of the Republican base are Christian voters, who ought to be at the tip of the spear of the fight against torture, but in practice seem to neither explicitly condone nor condemn it. But I'll be charitable and assume that the evangelical segment of the party is steadfast against torture, meaning that at least 2/3s of Republican voters are against torture. That leaves no more than 1/6th of the US population on board with torture. That's still pretty messed up, but I'm trying to be optimistic. :(
The most obvious case is getting a password. (or lock combo or crypto key, or anything else that you can verify) You torture until you get a password that works. Obviously, there should be good reason to believe that the person knows the password.
Another case is where you know many things but not everything. You ask about all that you want to know, including things you already know. The things you already know are the honesty check. Answers to the unknowns are assumed to be dishonest until you start getting correct answers for all the things you already know.