Of those surveyed, 35 percent say they are "very concerned" about violations of their personal privacy, while another 22 percent say they are "somewhat concerned."
The polling firm also found that nearly two-thirds of Americans report following the story closely, slightly higher than the average of other major news stories over the past two decades.
"The reactions to these types of government programs have remained constant over the past seven years, although Republicans and Democrats have essentially flipped their attitudes over that time period, reflecting the change from Republican President George W. Bush to Democratic President Barack ObamaBarack ObamaNew DNC chairman wastes no time going after Trump US weighs withdrawal from UN Human Rights Council: report GOP rep: We'd better have the votes to repeal and replace ObamaCare MORE," said Gallup's Frank Newport in a statement.
The Gallup poll is the latest in a series of surveys showing mixed opinion of the NSA surveillance controversy. A CBS poll released earlier Wednesday showed 58 percent of Americans thought the government should not collect the phone records of "ordinary Americans," but three-quarters said those same protections should not extend to suspected terrorists.
A Pew Poll released Monday 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 Gallup survey interviewed 1,008 adults between June 10-11 and carries a margin of error of plus or minus 4 points.