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 Feinstein (D-Calif.) and Speaker John Boehner (R-Ohio) have defended the NSA surveillance, while Sens. Rand Paul (R-Ky.) and Ron Wyden (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.