The program, which never got off the ground and remains shrouded in mystery, was designed to target leaders of the terrorism network at close range, rather than with air strikes that risked civilian casualties, government officials with knowledge of the operation said Monday.
The officials spoke on the condition of anonymity because they were not authorized to discuss it publicly. The program was canceled last month by CIA Director Leon Panetta shortly after he himself first learned of it.
Some Democratic lawmakers suggested the failure to notify the congressional intelligence committees violated the oversight laws, which require the intelligence community to keep Congress informed of its activities.
Cheney's direct involvement is fueling calls for an investigation, reports CBS News correspondent Nancy Cordes.
The leader of the House, Speaker Nancy Pelosi, said that House and Senate intelligence committees should "take whatever actions they believe are necessary to get more information on the subject," including whether Cheney played a direct role in proposing the secret program and withholding information from Congress.
Sen. Russ Feingold, a Democrat, joining the ranks of those calling for a thorough investigation, said, "Individuals who ordered that Congress be kept in the dark should be held accountable." Feingold said he had "deep concerns about the program itself," adding that he had written to President Barack Obama to ask for the probe.
Sen. Dianne Feinstein, a Democrat and the head of the Senate Intelligence Committee, has said that being kept in the dark by the CIA broke the law and "should never, ever happen again." But defenders of Cheney suggested that no laws were broken because the counterterrorism program never got beyond the talking stage.
"It's probably skirting the law," said CBS News legal analyst Andrew Cohen. "The question is what you do with that. And I don't think that there is going to be any will on Congress to prosecute him."
However, the issue might come down to whether any tax dollars were spent on the planning - and thus subject to congressional scrutiny.
It presented a delicate dilemma for the Obama administration, which so far has steered clear of joining congressional calls for thoroughly investigating controversial intelligence-community actions under President George W. Bush and Cheney and prosecuting those who broke the law.
Robert Gibbs, Mr. Obama's spokesman, continued on this careful path on Monday, saying Panetta was reviewing how keeping the information from congressional intelligence leaders "came to pass and I think that's wise."
"The president believes that Congress should always be briefed fully and in a timely manner in accordance with the law. Those are his beliefs as it relates to any of these programs," Gibbs said.
As to a related controversy, reports that Attorney General Eric Holder may be leaning toward having a criminal prosecutor look into whether U.S. interrogators tortured terror suspects, Gibbs repeated Mr. Obama's earlier statement that "our efforts are better focused looking forward than looking back."
Gibbs said the president as well as the attorney general and others in the administration "all agree that anyone who followed the law, that was acting in the good faith of the guidance that they were provided within the four corners of the law, will not and should not be prosecuted."
Panetta canceled the CIA program on June 23 after learning of its existence, its failure to yield results, and the fact that Congress had been unaware of it since its inception soon after the Sept. 11, 2001, terror attacks, according to one official with direct knowledge of the plan.
That official said Bush authorized killing al Qaeda leaders and that Congress was made aware of that. However, the official said, Panetta also told members of Congress that, according to notes that he had been given on the early months of the program, Cheney directed the CIA not to inform Congress of the specifics of the secret program.
Panetta told the committees there was no indication that there was anything illegal or inappropriate about the effort itself, the official said.
CIA directors since 2001 agreed with Cheney's decision not to inform Congress because the highly classified operation, described as "sporadic" and "embryonic," never managed to turn up the intelligence needed to carry out a kill and was not considered a covert operation, according to a former intelligence official. That official also was not authorized to discuss the program and spoke on condition of anonymity.
Congress has a right to know everything the CIA does, but the president can by law limit those told about covert operations to just the top four members of the House and Senate from the two parties and the senior members of the intelligence committees. Democrats on the House Intelligence Committee are pushing for a legal provision that would require the president to brief both committees in their entirety more often, but the White House has threatened to veto the move.
Most attempts to kill al Qaeda's leaders, believed to be hiding in Pakistan's troubled western border region, use armed drone aircraft because it is difficult terrain controlled by sometimes hostile tribes. But those strikes have sometimes killed and injured innocent civilians and caused outrage in Pakistan.
The government official said the CIA effort was meant to avoid such collateral damage.