"The president has said he's open to changes to this," Daley told CBS' "Face the Nation," in his first television interview since joining the Obama administration.
But Daley added that the president is "not open to refighting the entire fight of health care."
"People have suggestions on how to make it better," Daley said, "but he is not in favor of refighting this fight."
Daley also backtracked on his criticism he expressed last year regarding the president's health care reform law, arguing that his objections were with the "politics of the movement" as opposed to the content of the bill itself.
"I thought it was a very difficult climate to try to accomplish what they tried to," Daley told CBS' Bob Schieffer. "And I think the results, because of the misinterpretation of healthcare by many people, had a negative impact on Democrats."
"I absolutely believe, having been in business and hearing from business people, the importance of the need for the reform in health care," Daley continued. "It was the business community that was really saying to the politicians, 'This is costing us too much. It's too much of a wet blanket on the economy.'"
Daley also expressed dubiousness on a recent proposal by Republicans to cut $55 billion from the 2012 budget.
"You know, it's that old saying: 'Where's the beef?' Let's see exactly the cuts they're talking about," he said. "We all agree there must be cuts to this government. And again, you're going to see this President lay out a very substantial cut already."