Barack Obama, the US president, has previously dismissed calls for such a commission, saying he is more interested in "looking forward than I am in looking backwards", although he has stressed that "nobody is above the law".
Al Jazeera's Rosiland Jordan, reporting from Washington, said there was debate over whether those testifying before any commission should be granted immunity from prosecution and over how much access to government documents the proposed body would get.
"There is a sense on Capitol Hill that if criminal action was undertaken then those responsible should be punished," she said.
"There is also the competing concern of creating a major partisan rift in Washington when what they are really trying to deal with is the economic crisis.
"The last thing that the Democratic leadership on this issue ... wants to do is to do anything that would scare Republicans away from taking part in this panel."
In February, Leahy told The New York Times that he envisaged the commission as not being formed by members of Congress but by an outside group of people "universally recommended as fair-minded".
|Critics have called for the prosecution of
Dick Cheney, the former vice-president [AFP]
He also told the newspaper that he felt the commission should have the power to subpoena witnesses and possibly grant immunity for officials who testify truthfully, in a similar mould to South Africa's post-apartheid Truth and Reconciliation Commission.
A USA Today/Gallup poll conducted earlier in February found that 62 per cent of US citizens favour either a criminal investigation or an independent panel to look into allegations of torture.
Obama has rolled back some of the Bush-era national security policies, including the decision to close the US prison camp at Guantanamo Bay in Cuba.
However, some critics of the hearings say that Bush administration officials should face criminal proceedings.
Michael Ratner of the Center for Constitutional Rights told Al Jazeera that the commission was unlikely to achieve anything.
"I think it does nothing. It's almost a fraud. It gives an excuse to both sides of the aisle, Republicans and Democrats to say 'see, we've had a truth commission, no prosecutions, we'll get what can but most of it will be classified.'"
"There is sufficient evidence to begin a criminal investigation and a prosecution for torture. Cheney [former vice-president Dick Cheney] has said he was involved in waterboarding - we know that's torture. We know Rumsfeld [former defence secretary Donald Rumsfeld] is up to his neck in this stuff.
"What Leahy is doing is really deflecting a serious criminal investigation. It's completely insufficient."