The president was joined at the White House by Americans who said they had benefited from the Affordable Care Act.
The new healthcare.gov website, which sells medical insurance, is now working at acceptable levels after its disastrous launch, says the administration.
The act aims to provide health coverage to some 15% of US citizens who lack it.
Barack Obama sought to remind Americans that under his health programme, insurers can no longer deny coverage to those with pre-existing conditions, and young people can now stay on their parents’ coverage until age 26.
He discussed the intensive efforts to repair the healthcare.gov website, which has been a flop since it went online on October 1st.
“Today the website is working well for the vast majority of users,” Barack Obama said.
“More problems may pop up, as they always do when you’re launching something new. And when they do we’ll fix those, too.”
The White House is also due to hold a youth summit on Wednesday, in the latest attempt to promote the law among the young and healthy, a demographic crucial to the strategy of reducing overall healthcare costs.
It is part of a multi-pronged effort by the administration to counter the Republican argument that the act known on both sides of the political divide as ObamaCare is “a train wreck”.
The law’s problems have sent Barack Obama’s job approval ratings plunging and threaten to damage fellow Democrats in next year’s congressional elections.
Elsewhere in Washington DC on Tuesday, the White House’s chief of staff told a public policy forum that more than one million new visitors had logged on to healthcare.gov a day earlier.
Denis McDonough said the website’s new queuing system, used in times of high traffic, worked “pretty well”.
“No matter what, we’re going to see this thing through,” he said.
He did not provide updated figures for how many people had signed up for insurance plans.
The administration aims to enroll 7 million people in insurance plans before the end of March, when all Americans are required to have coverage or pay a fine.
But problems reportedly persist. Insurers say they are receiving enrolment forms that have errors or are duplicated, while others go missing altogether.
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