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While continuing to face deep skepticism from Republicans, President Obama and his team ran a victory lap of sorts Tuesday after declaring that more than 7 million people signed up for health insurance on the ObamaCare exchanges before the midnight deadline.

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"This law is doing what it's supposed to do. It's working," Obama said in the Rose Garden.

The president spoke pointedly to the law's critics, accusing them of trying to "scare people" and saying "there's no good reason to go back."

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

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    Republicans, though, made clear the debate is not over. "Despite the White House 'victory lap,' this law continues to harm the American people," House Speaker John Boehner's spokesman Michael Steel said. The speaker also renewed his call for the law to be repealed and replaced.

    The president on Tuesday touted the benefits of the program, including the economic security that comes with health insurance and protections that guarantee those with pre-existing conditions cannot be denied coverage. Earlier, White House Press Secretary Jay Carney said the total number of sign-ups by the midnight deadline was 7,041,000, not counting those given an extension and those who signed up late on state-run exchanges. Despite HealthCare.gov's technical problems and very rocky start, Carney credited a "remarkable surge in enrollment."

    Seven million was the original goal for the program. Still, administration officials were unable to answer key questions about the law and about the enrollment stats. Carney conceded that the administration does not have the "breakdown data" at this point.

    Unanswered is how many people have actually paid their premiums -- those who don't pay will not be considered enrolled. Also unclear is whether enough young and healthy people signed up to offset the cost of signing up older, less-healthy customers. And the administration still cannot say how many of those who enrolled via HealthCare.gov were simply people who had their old policies canceled because of the law.

    Republicans fighting against the law did not let up in the wake of the open enrollment period.

    House Budget Committee Chairman Paul Ryan, R-Wis., included a provision calling for ObamaCare's repeal in a House GOP budget plan on Tuesday.

    Boehner said the 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," he said in a statement. "Millions of Americans are seeing their premiums rise, not the lower prices the president promised.  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."

    Obama dismissed Republicans' concern about the law during his Rose Garden remarks, saying the "tall tales" have largely been debunked.

    "There are still no death panels. Armageddon has not arrived," he said.

    The president did not address the mix of those signing up for coverage though.

    While Obama has aggressively sought out 18-to-34-year-olds, some of the more recent reports show most of the enrollees are 35 and older.

    Yet the bigger question is perhaps whether the law has indeed helped insure at least some of the estimated 48 million Americans who previously did not have insurance or couldn't get it because of a pre-existing condition.

    The most recent finding by the often-cited McKinsey & Company shows 27 percent of enrollees were previously uninsured and that roughly 75 percent of those who signed up for private insurance under ObamaCare have paid their premiums.

    The White House and other supporters of the law were hoping for an enrollment surge that would confound skeptics.

    The insurance markets -- or exchanges -- offer subsidized private health insurance to people who don't have access to coverage through their jobs. The federal government is taking the lead in 36 states, while 14 other states plus Washington, D.C., are running their own enrollment websites.

    The Associated Press contributed to this report.