"It was a very tough decision for him. I know it was something which is difficult for him to do because he had and has respect for General McChrystal," Sen. Carl Levin, D-Mich., told CBS News chief Washington correspondent Bob Schieffer on "Face the Nation."
"But it was something that he thought needed to be done. I think generally there was a consensus around here, or near-consensus, that it was a fair and appropriate decision for a commander in chief to make."
Petraeus will face the Senate Armed Services Committee for his confirmation hearing Tuesday and there's little chance of anyone blocking his nomination, Levin said, but there are those within the Pentagon who are wary of the President's commitment to the counterinsurgency strategy in Afghanistan, even as he picked General Petraeus - the architect of 2007's troop surge in Iraq.
Coupled with the inflammatory comments made by McChrystal and his aides, questions were raised as to the overall relationship between the military and the White House.
CBS News national security correspondent David Martin wasn't surprised by the sentiments.
"I think that's what made this story such an instant firestorm," Martin said. "I think everybody who follows Afghan policy closely immediately recognized those sentiments as authentic. You do not have to go to Afghanistan to hear military officers complain about the civilian leadership. But they do it off the record. And they do not do it in a disrespectful way."
Martin said that the problem with the relationship is rooted in a lack of trust, "I think there's fundamental doubt on both sides," he told Schieffer. "The White House thinks (or is worried anyway) that the Pentagon is going to suck them in by continually asking for more troops . . . If we just get another 10,000 we can turn the corner. And the military simply is unsure that the president means it when he says he will do whatever it takes to succeed in Afghanistan."
Levin reaffirmed his own trust in the administration, saying, "I think his policy is the right policy. I think General Petraeus, who is the originator of a counterinsurgency policy - where your goal is to protect the population, basically, so that the population will turn on the Taliban and not support the Taliban, [and] work with the Afghan national army, which is so critical here - I think that's the right policy. It was the Petraeus policy. McChrystal supported that policy."
To Levin, the priority for Petraeus is to secure a takeover of command to the Afghan government and army: "The size and the strength of the Afghan army [are] critical. The Afghan army is popular in Afghanistan; our presence is not popular in Afghanistan. And our number one mission, it seems to me, and I think there's almost, there's a very strong support in our military for this, is to get the Afghan army to the point in terms of numbers, equipment, capability, that they can be the primary source of security for Afghanistan."
Levin said he believed Petraeus has "a very great capability of bringing people together. He has shown that he's able to bring together our civilian side in Afghanistan. He's shown that in Iraq when he was able to do that. And he's going to be able, I believe, to do that in Afghanistan.
"I would hope his relationship with our ambassador to Afghanistan is better than was the case with General McChrystal," Levin added. "I hope his relationship with our key State Department person there, Ambassador Holbrooke, will be better than was the case with General McChrystal, which was the source of some of McChrystal's staff grumblings. Yes, I think he can improve that situation."