The White House declared success Tuesday in meeting its goal of getting at least seven million Americans to sign up for new health insurance plans under the controversial Affordable Care Act.

U.S. President Barack Obama celebrated the milestone and touted his signature health policy's benefits during an address on the south lawn of the White House to an appreciative audience.

"This law is doing what it's supposed to do, it's working, it's helping people from coast to coast," the president said, adding that millions of Americans now have health insurance who couldn't get it before and others have more affordable coverage.

Obama thanked supporters for fighting for the law, also known as Obamacare, adding that it is something to be proud of and that they should keep defending against Republican attempts to dismantle it. The tall tales opponents told about the law haven't been proven, Obama said, and it's time for Republicans to stop fighting and accept the law is "here to stay."

Obama said the Affordable Care Act doesn't mean an end to all health care problems in the U.S. and that the law hasn't been perfect, but it's helping millions of Americans. “This law has made our health care system a lot better — a lot better,” he said.

He said many Americans still don't have insurance despite the law and that he's not done trying to make sure they can get it. “We’ll work to get more Americans covered with each passing year,” said Obama.

A contingent of procrastinating Americans waited until the last minute Monday to shop for and enrol in a plan before the midnight deadline. Since the enrolment period began last fall, 7,041,000 people signed up for health insurance through the federal exchange and thousands more signed up through a dozen state-run exchanges, White House spokesman Jay Carney said Tuesday afternoon.

He added that many more Americans have coverage through expanded Medicaid programs thanks to the ACA, or Obamacare as it’s also known, and an estimated three million young people have been able to stay on their parents' insurance plans for longer.

"I think it’s fair to say we surpassed everyone's expectations," Carney said after recounting the law’s difficult history, which has included a Supreme Court challenge, multiple attempts by Republicans to repeal it and a rocky rollout of the website in the fall that prevented people from signing up.

Healthcare.gov, the federal website handling the new insurance exchanges for most states, gave further ammunition to anti-Obamacare critics when it failed to work properly during the launch of the new health care initiative. The technical glitches were eventually worked out, but it took several weeks before it was running smoothly.

Website had glitches on final day

The site also had some technical glitches Monday, but it still had a record-setting day, with 4.8 million visits. Another 1.8 million people made telephone inquiries.

The numbers game with Obamacare is not over. There are still many more important figures to be tallied. How many young people signed up is important, for example, because it's believed that the payments paid into the plan by healthy, younger Americans will offset the costs incurred by their older counterparts and keep premiums down.

More than seven million people signed up but seven million have not yet paid their first month’s premium, and when Carney was asked about that, he suggested things are no different now than they were before the Affordable Care Act.

"People purchase health insurance, they have a premium to pay, and overwhelmingly, they pay them, on time," he said.

"I'd be disappointed if you suggested seven million wasn't a big deal."

It’s also not known how many people who signed up during this first enrolment period previously had no health insurance at all, or how many had insurance that was canceled, or how many people changed plans. 

The data crunching will continue in the days ahead, and Carney promised to release more numbers as they become available.

Republicans still fighting the law

Some Democrats, particularly ones who are up for re-election in this fall’s mid-term elections, have been shy to defend the ACA in their home states where it’s unpopular. But House minority leader Nancy Pelosi said Tuesday that her party is "proud" of what the law accomplished. 

Pelosi White House

House Minority Leader Nancy Pelosi of California speaks to reporters outside the West Wing of the White House in Washington, Tuesday, April 1, 2014, following her lunch with President Barack Obama. (Susan Walsh/The Associated Press)

"The number speaks to a healthy America," she told reporters after a meeting with Obama.

Republicans, meanwhile, are still promising to try and dismantle the law.

"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," House majority leader John Boehner said in a statement Monday afternoon.

"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. And taxpayers are being forced to pick up an unaffordable tab."

The next enrolment period is in November. The law stipulates that Americans without insurance are subject to a fine. The fine is $95 per individual.