(Bloomberg) -- Just more than 7 million people enrolled for insurance coverage under Obamacare after a last-minute rush to sign up by yesterday’s deadline, White House press secretary Jay Carney said.

The enrollment of 7.04 million people came after a “remarkable surge” in the final day of the open-enrollment period, which ended at midnight, Carney said. The figure doesn’t include enrollments through separate state exchanges or people who started the process and weren’t able to finish because of technical difficulties.

Also see Obamacare Sign-Up Ends as It Began With Crashes, Challenges

“It’s fair to say we surpassed everyone’s expectations,” Carney said at a White House briefing today.

He said the government doesn’t yet have a breakdown on the enrollees. President Barack Obama, who was told the figure this morning, is scheduled to deliver remarks on his signature health-care law at 4:15 p.m. Washington time.

Seven million enrollees matches the initial estimates for insurance sign-ups under the law. The Congressional Budget Office in February projected that 6 million people would enroll, after stumbles getting the federal website for enrollment up and running. The law has been under attack by Republicans, who are making dissatisfaction with Obamacare a central part of the congressional campaign for November’s elections.

Democrats ‘Pleased’

House Minority Leader Nancy Pelosi, speaking at the White House after meeting with Obama, 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.

A member of the House Republican leadership said before the announcement that Obamacare will still be an issue in the November elections.

“I don’t think the issue goes away at all,” U.S. Representative Tom Cole, an Oklahoma Republican, said on MSNBC. “I don’t see a lot of Democratic enthusiasm.”

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 exceeded the previous high of 1.8 million on Dec. 23.

Coverage Quality

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 be 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.

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