Poll: Most say government shouldn't collect phone records of 'ordinary Americans'

Americans also general believe the government has struck the right balance in its effort to fight terrorism. Just 36 percent say the government has gone too far in infringing on personal privacy, versus 46 percent who say the right balance has been struck and 13 percent who want additional government surveillance.

That said, nearly six in 10 Americans have some concern generally about their privacy being lost. But fewer than half describe themselves as "very" or "somewhat" concerned the government might be collecting their phone records or minoring their Internet use.

The poll also found that Americans are generally unconcerned that the public revelation of the NSA programs by 29-year-old defense contractor Edward Snowden would hurt anti-terror efforts. Six in 10 say the revelation did not weaken the United States's ability to prevent future attacks.

The complicated public opinion on the topic mirrors a fractured landscape in Washington, where strange pairings like Sen. Dianne FeinsteinDianne FeinsteinMeet the man who sparked the Democratic revolt on guns Post Orlando, hawks make a power play Ryan: No plans to vote on Democratic gun bills after sit-in MORE (D-Calif.) and Speaker John BoehnerJohn BoehnerCameras go dark during House Democrats' sit-in Rubio flies with Obama on Air Force One to Orlando Juan Williams: The capitulation of Paul Ryan MORE (R-Ohio) have defended the NSA surveillance, while Sens. Rand PaulRand PaulRepublicans question Trump's trip to Scotland Hate TV customer service? So does your senator Overnight Cybersecurity: Senate narrowly rejects expanding FBI surveillance powers MORE (R-Ky.) and Ron WydenRon WydenRepublican chairman: Our tax reform plan fits with Trump's vision Post Orlando, hawks make a power play Democrats seize spotlight with sit-in on guns MORE (D-Ore.) have expressed alarm.

It also provides new clarity to a Pew Poll, released Monday, that found 56 percent of Americans agreed the NSA phone record tracking was "an acceptable way for the government to investigate terrorism." Forty-one percent said it was unacceptable.

The CBS News poll was conducted June 9-19 among 1,015 adults, carrying a margin of error of 3 percentage points.

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