Updated

Senate leaders emerged Tuesday from a closed-door meeting with the National Security Agency chief saying the story about the American who leaked details about secret U.S. surveillance programs is enveloped in misinformation and called for public hearings.

“It’s not possible for Congress to do the kind of vigorous oversight that (President Obama) spoke about if you can't get straight answers," Oregon Democratic Sen. Ron Wyden said following NSA Director Keith Alexander’s meeting with members of the Senate Select Committee on Intelligence.

"It's appropriate now to have public hearings,” Wyden continued. “This will give the committee and the American people the opportunity to look at the disclosures that have come out here in the last 10 days or so. And I think that's the appropriate next step."

The closed-door briefing follows a  series of news stories about federal government programs that have been collecting information about millions, if not billions, of phone calls and Internet activities by Americans.

Edward Snowden, a 29-year-old American and NSA contract worker, claims to be the source for the stories.

Wyden’s remarks follow him calling into question this week why National Intelligence Director James Clapper said before the same Senate committee in March that he was not aware that the NSA  was “wittingly” engaged in such widespread date mining.

Florida Senator Marco Rubio emerged from the briefing saying some of the misinformation is the result of inaccurate reporting.

“Some of the things that I have read are not fully accurate or paint a complete picture of some of the safeguards or even how the programs work,” he said. “That being said, I understand why people are concerned.”

Much of the discussion also focused on contract workers having high-level security clearance.

"From a policy standpoint, I've long been concerned about the role of contractors in the intelligence field and that is surely an area that will be explored at considerable length in these hearings,” Wyden said. “And I'm going to do everything I can to make sure that we have those hearings promptly.”

Rubio acknowledged that leaks and federal contractors with security clearances have been an “ongoing concern” in Washington but did not discuss what steps lawmakers might be taking.

However, committee Chairwoman Dianne Feinstein, D-Calif., said after the meeting that she wants to re-evaluate intelligence contracting, specifically looking at reducing the number of contracts.

She also said declassifying information on NSA programs would show its benefits.

"We asked (Alexander) to declassify things because it would be helpful," Feinstein said.

Sources familiar with the briefing also told Fox News that lawmakers were concerned about more bombshell revelations on super-secret U.S. surveillance. They also said the committee, largely for the newer members, was briefed on the NSA-led program, code-name PRISM, that tracks such Internet activity as emails and instant messages.