But with a key deadline approaching fast, he urged some of his most steadfast backers to help sign up millions more by then.
"We've only got a few weeks left. March 31st, that's the last call," Obama said, explaining that anyone not signed up by that date will have to wait until open enrollment begins anew in the fall. In the meantime, they risk being fined for not having coverage.
The White House has set an unofficial goal of 7 million enrollees by the end of March.
Nearly 3.3 million people, or less than half the total, had enrolled through the end of January.
Enrollment was slowed at the start of the sign-up period last October by numerous glitches in the health care website the administration created to help people find coverage. Some states running their own websites encountered problems, too.
Obama blamed the depressed enrollment on the bungled website and on an "implacable opposition" that he said has spent hundreds of millions, if not billions, of dollars to oppose the signature domestic policy accomplishment of his presidency.
The president promised a "big push these last few weeks" to sign people up. Already, he and first lady Michelle Obama have talked up the health care law in interviews with radio and TV stations that reach largely black and Latino audiences. Vice President Joe Biden appeared Tuesday on "The View" to encourage its largely female viewership to help get people to buy coverage.
"If they want health insurance now, they need to sign up now," Obama said.
Besides the 4 million enrollees, Obama said millions more Americans were benefiting from the health care law's expansion of Medicaid as well as a provision that allows young people to stay on their parents' plans until they turned 26.
Signing up enough people, particularly those who are young and healthy, is critical for the insurance pool at the heart of the law to function properly by keeping premiums low for everyone.
Obama spoke to more than 300 activists at an Organizing for America summit at a Washington hotel. He later delivered a shortened version of his remarks to about 60 supporters at a by-invitation-only dinner in a nearby room.
Organizing for Action is an advocacy group founded by former Obama campaign aides and supporters.
Obama also sought his supporters' help to pressure Congress to raise the federal minimum wage for all workers. The president noted his recent action to raise the hourly minimum to $10.10 an hour for people working on federal contracts. But that will make a difference for just a few hundred thousand workers and not until the government awards new contracts or existing ones are renewed.
Obama said a majority of Americans of all political persuasions support a higher minimum wage.
"Let's get that minimum wage done and give America a raise," he said.
Two hours before the president spoke, his former Republican presidential rival, Mitt Romney, was seen in the hotel lobby. A Romney adviser said the former Massachusetts governor was in Washington to deliver a speech and was staying at the hotel by coincidence.
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