Appearing on "Fox News Sunday," Sen. Dianne Feinstein (D-Calif.), chairwoman of the intelligence committee, said Panetta told congressional leaders that Cheney ordered the agency to withhold details of the program from Capitol Hill. She called that a "big problem."
"I think that if the intelligence committees had been briefed, they could have watched the program, they could have asked for regular reports on the program, they could have made judgments about the program as it went along," Feinstein said. "That was not the case, because we were kept in the dark. That's something that should never, ever happen again."
She called the failure to brief Congress "outside the law."
Although the law requires that congressional committees be "kept fully and currently informed" on intelligence activities, there is some latitude for highly sensitive programs and routine ones.
Senate Majority Whip Richard J. Durbin (D-Ill.) told ABC's "This Week" that Congress should investigate whether Cheney or others ordered that the program not be disclosed to lawmakers.
Congressional leaders can protect the existence of secret programs, Durbin said. Not disclosing the program, he added, violated the Constitution's checks and balances.
"To have a massive program that is concealed from leaders in Congress is not only inappropriate; it could be illegal," Durbin said.
Responding to Durbin, Sen. Jon Kyl of Arizona, the Republican whip, said lawmakers must not "jump to any conclusions" and must remember that Cheney had a responsibility to protect national security.
Appearing on CNN, Sen. Judd Gregg (R-N.H.) said failing to notify top congressional leaders was inappropriate. But he accused Democrats of undermining the CIA through constant criticism.
"We have to have an extraordinarily robust and strong CIA," Gregg said.
"This national attempt by some of our colleagues on the other side of the aisle to basically undermine the capacity to protect and develop intelligence is, I think, going to harm us in the long run," he added.
Republicans also argued that a decision to appoint a special prosecutor to investigate CIA interrogators risked undermining American security by unnecessarily weakening the intelligence community.
"This is high-risk stuff," Sen. John Cornyn (R- Texas) told Fox News. "Because if we chill the ability or the willingness of our intelligence operatives and others to get information that's necessary to protect America, there could be disastrous consequences."