President: 7.1 million enrolled in Obamacare

People stand in the line to register to meet with Sunshine Life & Health Advisors, which is selling insurance under the Affordable Care Act at a store setup in the Mall of the Americas on March 31, 2014, in Miami.
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President Barack Obama announced Tuesday that 7.1 million people had enrolled in insurance plans sold on government-run exchanges by the close of Monday's sign-up deadline, just beating the original estimate officials made last summer.

"This law is doing what it's supposed to do, it's working," Obama said in remarks outside the White House, where he was met with sustained applause and cheers after announcing the tally, which he repeated several times, as if to savor the number.

"This law is helping millions of Americans, and in coming years it will help millions more," he said.

Obama's comments came a day after the close of open enrollment and five months after a disastrous roll-out of the federal Obamacare exchange raised questions of whether sign-ups would reach even half of the original estimates. That flawed launched left even some of the president's fellow Democrats suggesting that key provisions of the Affordable Care Act would have to be scrapped or delayed significantly.

Obama said that in addition to the more than 7 million people on the exchanges, millions more people have been newly covered under ACA provisions that expanded Medicaid eligibility for some low-income people, and 3 million adults under age 26 were added to their parents' plans under the law.

Obama also highlighted the fact that the ACA now prevents insurers from charging higher rates for people with pre-existing conditions or setting life-time caps on coverage, or different rates for women then men. He noted that under Obamacare, a slew of health benefits, including mammograms, contraception and preventative care, are now covered at no additional out-of-pocket cost by law. Those provisions apply to all insurance plans, not just those purchased on HealthCare.gov and other government exchanges.

"The bottom line is this, under this law, the share of Americans with insurance is up, and the growth of health-care costs is down, and that's good for our middle class, and good for our fiscal future," Obama said.

The president chided Obamacare critics for trying to repeal the law and using what he called scare tactics to turn people against the ACA. He said he would pressure governors who have opposed the expansion of Medicaid benefits in their states to reverse that decision, which has left millions of people without coverage they would otherwise qualify for.

"I don't get it," the president said. "Why are people working so hard for people not to have health insurance?"

He said, "Many of these tall tales about this have been debunked. There are still no death panels," which got a peal of laughter from the audience. "Armageddon has not arrived."

And, Obama said, to sustained applause, "The debate over repealing this law is over. The Affordable Care Act is here to stay."

The administration had been confident last summer that it would reach 7 million enrollees on the government-run exchanges. But that confidence shattered after HealthCare.gov and state-run exchanges launched in October, and it became obvious that the federal marketplace and several others had such bad technical problems that most people were unable to apply or enroll.

In November, the administration revealed that just 106,185 people had enrolled in all of the exchanges during the month of October—a whopping 79 percent below the enrollment the Congressional Budget Office had initially estimated would sign up that month. While November's tally was somewhat better, the exchanges still ended the month with only 365,000 enrollees, or nearly 50 percent below the CBO's original estimate.

Enrollment dramatically accelerated in December after a massive, weeks-long repair effort to HealthCare.gov began to bear fruit, and as the deadline for obtaining coverage by Jan. 1 approached.

But the initial failure of HealthCare.gov loomed large, so much so that the CBO several weeks ago adjusted its 7.066 million estimate downward to predict that only 6 million people would be enrolled via the exchanges by the end of this past Monday.

Read MoreThe Obamacare exchange tally: $36K per enrollee?

Source: Healthcare.gov

However, the Obama administration last week announced that it had already hit that target, and continued an intensive outreach and marketing effort to get people to sign up before Monday's deadline.

That effort bore dramatic results Monday, when 4.8 million people visited HealthCare.com, and more than 1 million people phoned the call center for the exchange.

At around 12:01 a.m. Tuesday, right after the exchange closed open enrollment, White House Chief Technology Office Todd Park told workers at the offices of QSSI, the tech firm that lead the HealthCare.gov repair effort, that the federal exchange alone had enrolled about 217,000 people on Monday, far in excess of any other single day's tally.

Park also announced that with those sign-ups, nationwide enrollment in Obamacare exchange plans had topped 7 million—the original milestone that had been abandoned.

Read MoreHealthCare.gov or bust! Millions flood Obamacare sign-up

The enrollment tally has come as somewhat of a surprise to both Obamacare proponents and critics.

"A month ago, I didn't think they'd make six million, so I stand corrected," said Douglas Holtz-Eakin, a former Congressional Budget Office director who now leads the Center for Health and Economy think tank.

Holtz-Eakin said that a key reason that Obama Administration was able to reach 7 million enrollees even in the face of a deeply troubled launch of the federal exchange last fall was experience gained during two successful presidential campaigns."The goal was always to use their very effective campaign turn-out operation as an enrollment operation," he said.

"In the same way they got people to the polls, they got people signed up."

But Holtz-Eakin said Obama "needs more than 7 million" enrollees for his health-care reform effort to succeed in the long run.

"Inside that 7 million they have some serious 'Swiss cheese," Holt-Eakin said.

In particular, questions remain about what percentage of enrollees will end up paying their first premiums, how many people who signed-up were previously uninsured, and how many people will serious health issues have enrolled in Obamacare plans.

"It's not an unmixed blessing to get some of these people to sign up," Holtz-Eakin said, referring to how too many sick enrollees can drive prices much higher for an insurance plan.

"The best guess is the exchanges turn out to be a federal 'high-risk' pool," he said.

Holtz-Eakin also the administration soon will be faced with the prospect of insurance premiums on the exchanges increasing by large amounts

"At the end of May, the insurers are going to file their rate plans for next year," Holtz-Eakin said. "I think everybody knows they lowballed [their rates this year] to get market share."

House Speaker John Boehner, R-Ohio, said vowed that House Republicans "will continue to work to repeal this law and protect families and small businesses from it's harmful consequences."

"The president's health care law continues to wreak havoc on American families, small businesses and our economy, and as I've said many times, the problem was never just about the website—it's the whole law," Boehner said.

"Millions of Americans are seeing their premiums rise, not the lower prices the president promised," Boehner said. "Many small businesses are afraid to hire new workers, instead cutting hours and dropping health coverage for existing employees. Many Americans can no longer see their family doctor, despite the pledge no one would lose access to their physician. Seniors are feeling the impact, losing their Medicare Advantage plans the president promised they could keep. And taxpayers are being forced to pick up an unaffordable tab."

Read MoreMaryland to drop its $125M Obamacare exchange

By CNBC's Dan Mangan