David Jackson and Aamer Madhani

USA TODAY

WASHINGTON — President Obama said Thursday that 7.1 million Americans have signed up for insurance under his new health care law, proving that "the Affordable Care Act is here to stay."

"This law is doing what it's supposed to do — it's working," Obama said in a celebratory ceremony with supporters in the White House Rose Garden.

Obama also denounced Republican attacks on the new system, claming that "the debate over repealing this law is over." If the GOP continues to pursue to repeal, Obama said Republicans will have to explain to millions of newly insured Americans why they want to take away their policies.

Instead, Obama urged Republicans to work with him in the months ahead to improve the law where needed, including expansion of Medicaid in states that have resisted the plan.

The new law hasn't "completely fixed our long-broken health care system," Obama said, but it has "made our health care system a lot better."

The end of the enrollment period for this year commenced a new struggle between the parties to define the landmark health care law, eight months before congressional elections.

Republicans who had questioned whether the administration could reach its enrollment goal vowed again to repeal and replace the law, saying it is creating higher premiums and worse health care.

Obama "is taking a premature victory lap for his signature health care law," said Republican National Committee Chairman Reince Priebus.

With the announcement that came hours after the March 31 deadline to sign up for coverage, the Obama administration has cleared the initial projection for enrollees set by the Congressional Budget Office — a goal that had seemed out of reach after a rocky launch to the online federal marketplace last fall.

"We surpassed the 7 million mark with the over 200,000 people who enrolled yesterday in states run by the federal government alone," White House Press Secretary Jay Carney said. "When we get numbers in from the rest of the states and people who are trying to sign up by the deadline and are finishing now, even more people will be covered."

After meeting with Obama at the White House on Tuesday, House Minority Leader Nancy Pelosi, D-Calif., cheered the administration crossing what was seen as a crucial threshold for the law.

"Many more people now have affordable, quality health care," Pelosi said.

After a surge of last-minute enrollment on Monday — the technical deadline to sign up for health care or face a penalty — administration officials began expressing confidence that they would meet or exceed the 7 million mark for signups.

In recent weeks, the White House had been buoyed by a surge of interest by Americans in the laws as the deadline for signing up drew near. There were 2.9 million visits to the website over the weekend, and last week they counted more phone calls from Americans inquiring about signing up for insurance that they saw in all of February.

Last-minute consumers overwhelmed the federal web site on deadline day as outages and intermittent delays slowed customers. More than 2 million people visited the web site by Monday evening.

Carney suggested that Obama had a hunch the administration would reach the 7 million mark as Monday approached. Early Tuesday morning, aides confirmed to him during his presidential daily briefing that the goal had been met.

Republicans continued to attack the law on Tuesday, arguing that too little is known about the 7 million enrollees, including how many were previously uninsured and how many have in fact paid the premiums.

GOP members vowed to maintain their repeal efforts, and to make health care a major issue in the November congressional elections.

Senate Minority Leader Mitch McConnell, R-Ky., said "our constituents are having an unpleasant interaction" with what he called "Obamacare."

"Whether they can sign up for a policy or not, they are discovering, of course, higher premiums, a higher deductible," McConnell said. "Many of them are losing their jobs and so it is really a catastrophe for the country both for the healthcare providers and the consumers."

Echoing McConnell, House Speaker John Boehner, R-Ohio, said that "the problem was never just about the website — it's the whole law."

Republicans also disputed Obama's claim they want to deny people insurance.

Boehner spokesman Michael Steel said people are "losing the doctors and plans that they like," and "we must replace this fundamentally-flawed law with patient-centered solutions that will actually lower health care costs and help create jobs."

In his White House remarks, Obama said that changing the law now will hurt people who have signed up, saying at one point: "Why are folks working so hard for people not to have health insurance?"

The president warned that there will likely be future "challenges" with with the law -- possibly including more website "stumbles" -- but lawmakers should work together to address them. Obama decried "tall tales" that Republican critics have invented about the law, and warned that "history is not kind to those who would deny Americans their basic economic security."

Democrats embraced Obama's announcement as hopeful news for re-election candidates who had been feeling the weight of the president's low popularity numbers and Republican attacks on the law.

Mo Elleithee, the Democratic National Committee communications director, noted that public opinion over the health care law has slowly been turning in favor of Democrats. On Monday, an ABC News/Washington Post poll found that support for the law hit a record high at 49%.

"For years, Republicans have been jumping up and down, breathlessly screaming that the Affordable Care Act would be a 'disaster,' " Elleithee wrote in an e-mail to reporters "Guess what? APRIL FOOL'S! The joke is on them."

Pelosi -- who attended Obama's speech along with other Democratic lawmakers -- predicted health care won't hurt Democrats at the polls.

Democrats are "proud" of the law, she said, and "our members are out there on the offensive on this issue."

She said jobs should be the main issue in the congressional elections, and she attacked the new Republican budget, which in part includes the GOP's repeated call to repeal the law.

The White House did not have a timeline for releasing demographics of enrollees, nor did the administration have figures for individuals who entered an online queue to shop for insurance but were unable to complete the sign-up process.

"We are not going to take our eye off the ACA ball," Carney said. "We have ...crossed an important milestone here, but it's not the finish line."