On Tuesday, White House press secretary Jay Carney defended the administration's approach.

"As you heard the President say on Friday, he believes that we must strike a balance between our security interests and our desire for privacy," Carney said. "He made clear that you cannot have 100 percent security and 100 percent privacy, and thus we need to find that balance. He believes as commander in chief, that the oversight structures that are in place to ensure that there is the proper review of the kinds of programs that we have in place, authorized by Congress through the Patriot Act, and FISA [Foreign Intelligence Surveillance Act] do strike that balance."

Still, Americans are generally satisfied with the job Obama is doing protecting the country from the threat of terrorism. Of those surveyed, 29 percent say Obama is doing a good job, 16 percent say he's doing an excellent job, and 20 percent say the president is doing a fair job. Conversely, 29 percent say Obama is doing a poor job.

The HuffPost/YouGov poll was conducted June 7-8 and surveyed 1,000 adults. The polling firm did not provide a margin of error.