"I think he understood that the debate was veering off in the wrong direction and as he said, that his words may have contributed to that, so he felt a responsibility to step forward and kind of cool the situation," Axelrod told CBS' Bob Schieffer.
Axelrod noted that when President Obama said the Cambridge Police Department acted "stupidly" during a press conference Wednesday night, "he calibrated his words poorly."
He applauded his boss for addressing the issue during a surprise visit to the daily press briefing Friday.
"I think it has had the desired effect. I think people are talking more constructively now and I think the steam has gone out of this," he told Schieffer.
Asked about the president's invitation for the arresting police officer and Professor Gates to have a beer with him at the White House, Axelrod said, "They expressed an interest in coming and coming to the White House and, you know, I think that will likely happen."
On the health care bills, which are stalled in the House of Representatives and the Senate partly due to conservative Democrats' concerns, Axelrod said there is agreement on "eighty percent" of the issues, and that the White House and Congressional leaders are working through details of the remaining "twenty percent."
Asked if President Obama will at some point have to lay down some specifics which he wants to see in health care reform, Axelrod said the president has "almost daily, perhaps dialogue hourly in the last few months" dialogue with members of Congress on the issue.
"The president did lay out a very specific array of cuts and savings that will help finance most of this health reform, and those have been largely embraced by everybody on top, so he is involved in the process and will continue to be in steering the right direction - that it lowers costs and improves quality of care and get us out from under the yoke of this inexorable climb in healthcare costs."
Schieffer asked whether President Obama is prepared to tax, "gold-plated Cadillac insurance policies."
Axelrod said the objective is to keep the "burden off the middle class who are struggling in this economy," and that options for the bill will be weighed on that basis. "If it meets that test, then he will certainly give it consideration, and I think that is certainly a possibility.
"The fact is everyone is focused on the fact that we have some issues left to resolve. We made enormous progress on this and I think we will continue to do that, and it will be a target to get something done in the fall on this, which has always been, you know, our goal," he said opitimistically.