Today, Cheney's daughter and former State Department official Liz Cheney defended her father's views on enhanced interrogation techniques and assailed the Obama administration for not releasing the classified intelligence memos her father requested.
The memos, the Cheneys say, show that techniques like waterboarding yielded valuable information from detainees.
Last month, the Department of Justice released memos showing the legal justification for waterboarding -- an interrogation tactic that simulates drowning -- written by Bush-era officials.
Releasing those memos gave "terrorists a new insert for their training manual," said Liz Cheney on "Good Morning America," echoing remarks her father made yesterday at the American Enterprise Institute. "It takes a tool out of the toolbox for every future president."
On the contrary, Lawrence O'Donnell, former Senate Democratic chief of staff, argued that policies of the Bush-Cheney administration actually made the country less safe.
"It is torture. This government has prosecuted people in the past for doing exactly this," O'Donnell said on "GMA." "He [Dick Cheney] can never acknowledge what waterboarding actually was as practiced by the Bush administration."
"If [it was] so effective, why did they use it only on three?" questioned O'Donnell. "Why didn't they use it on the 500 people the Bush-Cheney administration released from Guantanamo -- 75 of whom we know ... have gone back into the terrorism business."
The waterboard was used on three prime terror suspects held in Guantanamo Bay.
The president argued Thursday that his predecessor's policies on terrorism made the country less secure. He affirmed that he considered waterboarding torture and said techniques such as those not only made the United States less safe, they were also against American values.
"I know some have argued that brutal methods like waterboarding were necessary to keep us safe. I could not disagree more," the president said in his speech at the National Archives. "As commander in chief, I see the intelligence. I bear the responsibility for keeping this country safe. And I categorically reject the assertion that these are the most effective means of interrogation."
In another part of town, Cheney argued the opposite.
"I was and remain a strong proponent of our enhanced interrogation program," the former VP said. "The interrogations were used on hardened terrorists after other efforts failed. They were legal, essential, justified, successful, and the right thing to do."
Obama also assailed the Bush administration for employing an ideology of fear rather than sound principles.
"We are indeed at war with al Qaeda and its affiliates," the president said. "We do need to update our institutions to deal with this threat. But we must do so with an abiding confidence in the rule of law and due process; in checks and balances and accountability."
"Too often, our government made decisions based upon fear rather than foresight, and all too often trimmed facts and evidence to fit ideological predispositions," he said.
Cheney -- as he has argued vehemently in recent months -- said the Bush administration's strategy was successful.
"You can look at the facts and conclude that the comprehensive strategy has worked, and therefore needs to be continued as vigilantly as ever," he argued.
"Critics of our policies are given to lecturing on the theme of being consistent with American values, but no moral value held dear by the American people obliges public servants to sacrifice innocent lives to spare a captured terrorist from unpleasant things. And when an entire population is targeted by a terror network, nothing is more consistent with American values than to stop them," Cheney said, offering a starkly opposing view to that of the president.
Obama gave a professorial explanation on why his administration needed to reverse the Bush Administration policies that "established an ad hoc legal approach for fighting terrorism that was neither effective nor sustainable."
In a speech that ran nearly 50 minutes, Obama laid out his case for ending so-called enhanced interrogation methods, closing the detention center at Guantanamo Bay and moving detainees currently held there. He stressed that he inherited these complex legal and ethical questions from the previous administration.
"We are cleaning up something that is -- quite simply -- a mess; a misguided experiment that has left in its wake a flood of legal challenges that my administration is forced to deal with on a constant basis, and that consumes the time of government officials whose time should be spent on better protecting our country," he said.
Cheney took a shot at the president's decision to shut down the detainee center.
"I think the president will find upon reflection that to bring the worst of the worst terrorists inside the United States would be cause for great danger and regret in the years to come," he argued.
The Congress this week rejected $80 million from the war funding bill to help pay to shutter the detainee center. Some Democrats argue that the president needs to show them a more comprehensive plan on how his administration plans to shut down the facility, and what they will do about the more than 200 prisoners housed there.
Obama argued yesterday that Guantanamo Bay's existence has in fact created more terrorists rather than help American national security.
He added that the toughest issue facing his administration, and the one that is causing him headaches from Republicans and Democrats on Capitol Hill, concerns the detainees at Guantanamo who cannot be prosecuted but also cannot be released because of the threat they pose.
The president did not lay out a specific plan for these terror suspects but said there must be "clear, defensible and lawful standards for those who fall in this category."
"We must have fair procedures so that we don't make mistakes. We must have a thorough process of periodic review, so that any prolonged detention is carefully evaluated and justified," he said.
Some Republicans are capitalizing on Democratic lawmakers' hesitance to go along with the White House's plan to shutter Guantanamo Bay's detainee center.
"His persistent reminders that he 'inherited' these problems are unproductive and trite. Americans are looking for leadership, not finger pointing and excuses for the implementation of ill-advised policies," said chairman of the National Republican Senatorial Committee, Sen. John Cornyn, R-Texas, Thursday. "I think the vice president is controversial in some quarters, but there is nobody that knows better than he does about what the threats are that face our nation and why it was necessary to take extraordinary measures to protect our country."
House Minority Leader John Boehner, R-Ohio, said the president needs to prevent an alternative plan.
"Let me just state right up front that Republicans oppose releasing these terrorists or importing them into our local communities. I've supported the president's approach to Afghanistan and with regard to Iraq. But I think on this one, he's dead wrong," Boehner said.
"I am confident. I'm confident that this administration will do what it has done since being inaugurated, pursuing a very thoughtful, considered path to address challenges confronting the country," Rep. Steny Hoyer, D-Md., said about Obama's decision to shut down the detention facility.
ABC News' Jonathan Karl and Jake Tapper contributed to this report.