Just 28 percent said the tactics—denounced as torture and banned by President Barack Obama after he took office—"went too far and were wrong."
Those sentiments help explain why Obama has walked a fine line on the issue, declining to seek prosecution of those who conducted or authorized the interrogation tactics even as he has vowed they won't be used again. Even so, a 45 percent plurality of Americans said it would be acceptable for them to be used in the future.
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Amid new threats from the Islamic State that have caused Obama to revamp his policies toward Iraq and Syria, the survey suggests political limits for Democrats in 2016 in catering to the intense opposition of their party's liberal base toward more aggressive stances in the battle against terrorism. The survey's margin for error on the terrorism question is 4.4 percentage points.
Full results from the NBC/WSJ poll will be released Wednesday morning.
—By CNBC's John Harwood. Follow him on Twitter: @JohnJHarwood