Leahy was responding to a report in the New York Times that Cheney ordered the Central Intelligence Agency to withhold information about a secret counterterrorism program from Congress.
He said finding out what happened is important because "usually if something is done wrong by one [administration] and it's exposed, the next one tends to behave themselves."
Republican Senator Jeff Sessions of Alabama, meanwhile, noted that the Times' report was tied to anonymous sources.
"Sometimes leaked stories from unnamed sources don't turn out to be quite what they appear to be," he said. "Maybe they don't know the full facts and so forth on these matters."
Asked if Cheney's possible role in concealing a secret program should be looked into, Sessions said, "I'm sure it will be.
"I don't know what the facts are, but I believe that Vice President Cheney served his country with as much fidelity as he could possibly give to it, and he tried to serve us in an effective way," Sessions said.
"I hope nothing like this will impact on his outstanding record."
"It's either true or it's not true," responded Leahy. "I'd like to know if it's true or not. I mean, nobody in this country is above the law."
Leahy invoked the Abu Ghraib prison scandal and lamented the fact that those punished were lower-level figures as opposed to those who "condoned" or perhaps ordered policies that led to the abuse of prisoners.
"There was no evidence that the higher-ups participated in any way," Sessions replied, adding that one Abu Ghraib defendant said "there would have been hell to pay" had they known what was happening.
"It was an unusual event and the military did the right thing in prosecuting the people who were responsible," he said.
More from Face The Nation (7.12.09):
To watch Senators Leahy and Sessions debate Sotomayor, Cheney and investigations, click on the video player below.
Click on the video player below to watch a roundtable discussion, featuring Kevin Merida of the Washington Post and syndicated columnist Kathleen Parker, about a possible investigation into the Bush administration's use of torture tactics and its concealment of a CIA program from Congressional overseers.