"The demand is there," he said. "The product is good."
Still, it is too soon to say if the widely panned health-care rollout had turned a corner for good. The HealthCare.gov website was down for part of the day Friday as technicians attempted to fix an error that occurred Thursday night when the site was undergoing routine maintenance.
Additionally, the administration has had to enact several delays and exemptions for businesses and individuals, including one Thursday for some people whose health insurance policies were canceled because of the law's new standards.
No one in the administration is known to have been fired over the health-care failures. There have been repeated calls for the ouster of Health and Human Services Secretary Kathleen Sebelius, but Obama gave no indication Friday if he is considering that.
Other disputes lie ahead. Obama renewed his long-standing statement that he will not negotiate concessions with Republicans in exchange for legislation that will be needed in late winter or early spring to raise the nation's debt limit.
"It is not something that is a negotiating tool. It's not leverage. It's a responsibility of Congress," he said, although he added that he is willing to discuss other issues.
On a key foreign-policy concern, Obama said it would be wrong to impose new sanctions on Iran at a time when the United States and other nations are testing an interim accord designed to curtail Tehran's nuclear program. If necessary, "we can pass new sanctions in a day," he said, referring to lawmakers.
The president also addressed his decision to include openly gay athletes in the U.S. delegation to the Winter Olympics in Russia, which has a national law banning "gay propaganda." Obama said the delegation, which includes athletes Brian Boitano, Billie Jean King and Caitlin Cahow, shows the United States doesn't make distinctions on the basis of sexual orientation.
The Sochi Games are the first since 2000 to which the United States is not sending a president, former president, first lady or vice president. That decision has been seen as an indication of Obama's increasingly tense relationship with Russian President Vladimir Putin.
After the news conference, Obama and his family were to depart for Hawaii. It's the first year that last-minute legislative wrangling has not prevented the president from departing on schedule.
Obama did leave behind a New Year's resolution before boarding Air Force One.
"My New Year's resolution," he said, "is to be nicer to the White House press corps."