(CNN) -- Lawmakers who are now expressing outrage over the government's surveillance of phone records and Internet activity should have paid closer attention when they were voting to reauthorize provisions in the Patriot Act, Sen. John McCain, R-Arizona, said Sunday.

Reacting particularly to fellow Republican Sen. Rand Paul's assertion this week the programs amount to an "assault on the Constitution," McCain told CNN chief political correspondent Candy Crowley that members of Congress had not been left in the dark on what powers to government has in monitoring Americans.

"The Republican and Democrat chairs, and ... members of the Intelligence Committee have been very well briefed on these programs," McCain said. "We passed the Patriot Act. We passed specific provisions of the act that allowed for this program to take place, to be enacted in operation. Now, if members of Congress did not know what they were voting on, then I think that that's their responsibility a lot more than it is the government's."

Paul, a Kentucky Republican who enjoys support from a large bloc of libertarians, was elected to the Senate in 2010, years after the Patriot Act was first passed. However, the key provisions of the act that have been subject to scrutiny this week were reauthorized in the past two years.

In 2011, when Congress was debating the re-authorization of Section 215, Paul offered amendments that would have limited the government's powers of surveillance.

Section 215 allows the FBI to apply to the Foreign Intelligence Surveillance Act court -- FISA court -- to issue orders granting the government access to any tangible items in foreign intelligence, international terrorism and clandestine intelligence cases. It's the measure cited this week in a leaked document that revealed the Obama administration obtained a secret court order for phone records from Verizon.

Some lawmakers from both parties say they're worried the government's interpretation of the law - and not the law itself - is being kept secret from members of Congress. McCain argued Sunday for continuing the practice of only briefing intelligence committee members on top secret actions taken by U.S. agencies.

"I don't think the 535 members of Congress should be briefed on every program that our government is engaged in. That's why we have intelligence committees," McCain said, adding he would be open to involving the rest of Congress on some additional discussions of intelligence gathering.

"But we ought to be careful that we don't discuss practices that we employ that would help the enemy evade our detection and apprehension," he said.

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