Any investigation into interrogation practices might also be matched with an investigation of Cheney's actions.
The New York Times reported today that Cheney ordered the CIA not to tell Congress about the counterterrorism program. Obama's CIA director Leon E. Panetta learned of the program on June 23 and immediately ended it. He then briefed House and Senate intelligence committees the next day in private sessions, The Times reported.
On ABC's "This Week," Majority Whip Sen. Richard Durbin, D-Ill., argued the Senate Intelligence Committee should "absolutely" investigate the matter.
"To have a massive program that is concealed from the leaders in Congress is not only inappropriate it could be illegal," Durbin said.
"The executive branch of government cannot create programs like these programs and keep Congress in the dark," he added. "There is a requirement for disclosure, it has to be done in an appropriate way so it doesn't jeopardize our national security."
However, Senate Minority Whip Jon Kyl, R-Ariz., argued against any investigation just yet.
"I don't think we should be jumping to any conclusions," Kyl said. "The Republican leader on the intelligence committee in the House described this certainly not as some kind of massive program but something that was on again off again … never got off the ground."
Kyl said he understands the concept that national security concerns may preclude the executive branch from sharing some information with Congress.
"The president and the vice president are the two people who have responsibility ultimately for the national security of the country," he said.
Cornyn, a Republican, said on "Fox News Sunday": "To trot out the vice president and say he's the one that's at fault … this is unfortunately sounds like a new theme where they still want to blame the Bush-Cheney administration."
But Democrat Fienstein said on the same show that this should never happen again.
"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," she said. "That was not the case because we were kept in the dark."