The ABC News/Washington Post poll released Wednesday found 58 percent supported, and 39 percent opposed, the NSA collecting "extensive records of phone calls, as well as Internet data related to specific investigations, to try to identify possible terrorist threats."
Democrats and liberals supported the surveillance programs far more than Republicans, the survey found.
However, 65 percent of Americans, regardless of political ideology, said they wanted congressional hearings on the issue.
People are sharply divided over whether to prosecute Edward Snowden, the government contract worker who revealed details about the secret programs. Forty-three percent want to charge him with a crime, while 48 percent said they opposed charges.
Opinions favoring Snowden's prosecution were strongest -- 56 percent -- with people who described themselves as very conservative, while 58 percent of those younger than 30 said he shouldn't be charged.
The findings are contrary to surveys conducted during the administration of George W. Bush, under whom the programs began. An ABC/Post poll then found most Republicans and conservatives felt the surveillance was necessary to combat terrorism, even at the cost of privacy. Liberals and Democrats thought privacy was more important.
The latest poll was conducted June 12-16 in English and Spanish among 1,017 adults. The margin of error was calculated at 3.5 percentage points.