Obama said there will be more stumbles and that all the flaws in the health-care system haven't been fixed.

"Change is hard. Fixing what's broken is hard. Overcoming skepticism and fear of something new is hard," Obama said. "But this law is doing what it's supposed to do."

He said opponents are criticizing "without offering any plausible alternative."

Republican Critics

The law has been under attack by Republicans, who are making dissatisfaction with Obamacare a central part of their congressional campaigns for November's elections.

Republican Representative Paul Ryan of Wisconsin called the enrollment figures "a Pyrrhic victory." Republicans still plan to offer alternative legislation to replace the Affordable Care Act, he said.

Other Republicans questioned how many of those who signed up have actually paid premiums for coverage, cited the continued rise in health-care costs and the cost to businesses.

"Every promise the president made has been broken: health care costs are rising, not falling," Michael Steel, a spokesman for House Speaker John Boehner said. "Americans are losing the doctors and plans that they like."

Milestone's Impact

While reaching 7 million enrollees represented a political victory for the president, it may not be enough to turn around his lagging second-term fortunes.

Democrats remain at risk of losing control of the Senate in November. The president's approval ratings are stuck in the 40s, with Gallup's latest three-day tracking poll showing 44 percent of Americans approve of his performance while 51 percent disapprove.

House Minority Leader Nancy Pelosi, speaking at the White House after meeting with Obama earlier today, said Democrats "are very pleased with the ACA results," and that the party's candidates won't be running away from the issue.

"Overwhelmingly, our members are out there on the offensive on this," the California Democrat said.

Even with the high turnout seen at the Obamacare exchanges over the past week, Americans remain split on the law with about 49 percent in support and 48 percent opposed, according to an ABC/Washington Post poll of 1,017 Americans.

Final Push

There were more than 4.8 million visits to HealthCare.gov yesterday, the end of the first open enrollment period, according to the Centers for Medicare and Medicaid Services, a unit of the Department of Health and Human Services. That far exceeded the previous high of 1.8 million on Dec. 23.

Attention now will turn to the quality of coverage Obamacare enrollees receive, their access to medical services, and insurer preparations for 2015.

Already, Indianapolis-based WellPoint Inc., the largest exchange insurer, has warned it may propose "double-digit plus" premium increases for the next enrollment period, which begins in November. Insurers must quickly assess the medical demands of their new customers before filing rates at the end of May.

Determining the success of the system may take a while, according to the Congressional Budget Office. The CBO, which estimates that 45 million Americans will remain uninsured this year despite the law, says that number will only shrink as far as 31 million by 2024, the 11th year of expanded coverage.

The percentage of uninsured nonetheless has fallen since the law was passed in 2010, according to a Gallup Poll survey. In the first quarter of 2014, the rate fell to 15.9 percent, its lowest quarterly level since 2008.

–With assistance from Kathleen Hunter, Roger Runningen and Alex Wayne in Washington.