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The senator, who linked a video of the exchange last week on Twitter, asked Mr. Clapper whether the government collects data on millions of Americans. The director said it does not, at least not wittingly.

But Edward Snowden, a 29-year-old former analyst with the contracting firm Booz Allen Hamilton — who also worked for the CIA and NSA — set off a firestorm last week by telling The Guardian newspaper that the NSA keeps data records on phone calls from Verizon customers and collects Internet data from foreigners through a previously secret program known as Prism.

This week, Mr. Clapper told NBC’s Andrea Mitchell that he answered Mr. Wyden’s question “in what I thought was the most truthful, or least untruthful manner, by saying no.”

Mr. Wyden said oversight of the nation’s intelligence agencies “cannot be done responsibly if senators aren’t getting straight answers to direct questions,” Mr. Wyden said in a prepared statement.

But Sen. Lindsey Graham, South Carolina Republican, who isn’t a member of his chamber’s intelligence committee, said any member of Congress who pleads ignorance of the program “has got nobody to blame but themselves.”

“It was there to be learned about, it was there to be understood. So when somebody who’s been in Congress for any length of time is upset and astonished and appalled, somebody needs to ask them, in your business, why didn’t you know about this program?” Mr. Graham told a group of reporters at the Capitol.

“I’ve never felt like I’ve been shut out of the process when it comes to what we’re doing to protect ourselves.”

Mr. Graham added that he would be fine with certain security briefings being expanded beyond the two intelligence committees.

Since the NSA snooping program broke, both chambers have held chamberwide briefings on the situation, including a closed-door House meeting Tuesday.

Meanwhile, lawmakers cited Mr. Snowden — who leaked information about the NSA’s telecommunications surveillance program — as a consequence of a bloated, expensive contracting workforce.

“The story that’s told is that he was a high school dropout, that he didn’t finish his military obligation, though he attempted, and dropped out of community college. And it’s also reported that he’s being paid in the range of $200,000 a year as a contract employee,” Senate Majority Whip Richard J. Durbin, Illinois Democrat, said at a Senate Appropriations Committee hearing.

Booz Allen said Tuesday that it fired Mr. Snowden, who is believed to be hiding in Hong Kong. Mr. Snowden earned about $122,000 a year, the consulting firm said.

“I continue to be concerned about the cost of the contractor workforce, not just in the NSA but in the Department of Defense,” said Mr. Durbin, chairman of the panel’s defense subcommittee.

Tom Howell Jr. and Kristina Wong contributed to this report.