Cohen, a top adviser to Bush-era Secretary of State Condoleezza Rice, has been a vocal Trump critic.
In an exchange with New York Democratic Sen. Kirsten Gillibrand, the lone member of the SASC who has voiced opposition to the waiver, Cohen said he believed Mattis could stand up to Trump if he gave an illegal order to use torture.
"As a candidate, the president-elect indicated he would use torture not only against suspected terrorists, but their families," Cohen said. "It's not only outrageous, its illegal, its profoundly immoral—and I think Secretary Mattis would refuse to comply, and that's extremely important."
Since Mattis retired in 2013, he will need Congress to carve out an exception to national security rules mandating a seven-year "cooling off" period for retired military to take over the top civilian defense job.
In a November interview with the New York Times, Trump said Mattis gave him a new perspective on waterboarding, a torture tool he pledged on the campaign trail to reinstate.
"He said — I was surprised — he said, 'I've never found it to be useful.' He said, 'I've always found, give me a pack of cigarettes and a couple of beers and I do better with that than I do with torture.' And I was very impressed by that answer," Trump said.
Kathleen Hicks, an expert at the Center for Strategic and International Studies, said, "Gen. Mattis could be a very strong figure" on a Trump national security team worryingly dominated by generals and lacking in career diplomatic skills. She too was reassured Trump had listened and absorbed Mattis's views on torture.
"The president-elect, in at least one instance that we know of quite publicly, listened … to the advice of Gen. Mattis with regard to a viewpoint on illegal torture," Hicks said. "My view is that he could play a helpful role in this administration."
Hicks also called Mattis a candidate with "an expert grasp on the most important security issues facing the nation" and praised his "embodiment of the principles of civilian control of the military."
But she also warned that lawmakers should grant a waiver based on those kinds of considerations, and not on an excessive trust of military experience. Hicks found "deeply troubling" Trump's take on Mattis — voiced in that New York Times interview — that "it's time for a general."
The praise for Mattis came with a warning that the US must protect the civil-military balance that undergirds US democracy.
Other countries that have had retired generals in similar roles, like Israel, have suffered from a politicized senior officer corps, according to Cohen. Israel's politics are are often roiled by active-duty and retired generals, he said.
Lawmakers seem poised to grant Mattis a waiver, based largely on his resume and expressed understanding of civilian control of military issues.
On Thursday, Mattis will appear before the SASC for his confirmation hearing and the House Armed Services Committee for its hearing on the civilian-military relationship. Both committees are expected to consider and advance the waiver legislation that day, and from there would get a vote in both houses. Senate Majority Whip John Cornyn, R-Tex., said Monday the waiver could be moved to the Senate floor that same day.
In the SASC hearing Tuesday, SASC Chair John McCain, R-Ariz., said he "will fully support" the one-time waiver for Mattis, "an exceptional public servant worthy of exceptional consideration." Mattis, McCain said, has an exception grasp of the civil-military relationship.
"He has upheld the principle of civilian control of the armed forces in four decades of military service as well as in civilian life," McCain said.
The committee's top Democrat, Sen. Jack Reed, of Rhode Island, has not committed to a position. On Tuesday, he worried about inadvertently politicizing the armed forces, which could fuel suspicion of military leaders by Congress and a further erosion of civil-military relations.
"During this past presidential election cycle, both Democrats and Republicans came dangerously close to compromising the nonpartisan nature of our military when the nominating conventions featured speeches from recently-retired general officers advocating for a candidate for president," Reed said.
Reed also warned Trump's selection of retired senior military officers could bring about the militarization of national security policy. In addition to Mattis, Trump has nominated recent retirees Gen. John Kelly to lead the Department of Homeland Security, and Lt. Gen. Michael Flynn as national security advisor.
"Diversity of opinion is important when crafting policy and making decisions as weighty as those facing the next administration," Reed said.
Military Times Leo Shane III contributed to this report.