At first blush, it seemed, most Americans haven’t gotten too exercised about the revelation that the National Security Agency has been secretly tracking everyone’s phone data, in the name of protecting national security.

That was the take-away from a Washington Post/Pew Research Center poll released Tuesday. But two new polls out Wednesday – one by Gallup, another by YouGov taken for The Economist – paint a difference picture. Both find that a majority of Americans disapprove of the NSA data-mining programs.

In the Gallup poll, conducted June 10 and 11, 53 percent of Americans disapprove of the programs, while 37 percent approve. YouGov found that 59 percent disapprove of the programs, and only 35 percent approve.

Americans are also skeptical that the snooping is doing much good. Per YouGov, only 35 percent say it’s likely the information has prevented a terror attack, while 54 percent doubt it has. And while President Obama insists that “nobody is listening to your phone calls,” it turns out only 17 percent of Americans think that’s true, according to the YouGov poll, taken June 8 to 10.

“Reading your emails, listening to your phone calls, examining your phone or computer without a warrant – those are intrusions rejected by large majorities approaching the 93 percent who insist on seeing a warrant, subpoena, or national security letter before they'd consent to allowing government to enter their homes without permission or probable cause,” YouGov says in its report on the poll.

In another small hint at how some Americans are reacting to the data-mining stories, Bloomberg News reports that sales of George Orwell’s book “1984” have spiked on Amazon.com. The 1949 classic, a staple of high school reading lists, depicts a dystopian society marked by near-saturation surveillance at the hands of Big Brother.

Others have taken to putting their name on a “We the People” petition at WhiteHouse.gov. As of 3:41 p.m. Wednesday, 63,532 people had signed on to a petition demanding the pardon of Edward Snowden, the former NSA contractor who says he leaked top-secret documents about government surveillance programs to The Guardian and The Washington Post. The petition needed 48,000 to merit a White House response.

“Edward Snowden is a national hero and should be immediately issued a full, free, and absolute pardon for any crimes he has committed or may have committed related to blowing the whistle on secret NSA surveillance programs,” the petition reads.

Mr. Obama prides himself on running a transparent government and says he welcomes a public debate about where to draw the line between protecting public safety and safeguarding civil liberties. But given that the antiterror surveillance programs remain largely secret, it’s not clear just how much will be debated in public.

Many members of Congress, from both parties, are defending the surveillance programs. But even some of the president’s allies are calling for more transparency.

“The president or his people need to be more forthcoming,” Sen. Mark Begich (D) of Alaska told Politico. “Look, we understand the need for secrecy, I get it, but the fact is we also need a lot more transparency on the process.”

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Senator Begich is in a bipartisan group of eight senators that is calling on the White House to declassify legal decisions that have allowed widespread phone and Internet surveillance, as revealed in the recently leaked documents.

Speaking at a congressional hearing Wednesday, the director of the NSA, Gen. Keith Alexander, said that the secret surveillance of phone data has helped prevent dozens of terrorist events. He promised that records about those thwarted attacks would be made public within a week.