(Recasts with Obama comments, details throughout)
By Jeff Mason and Mark Felsenthal
WASHINGTON, April 1 (Reuters) - President Barack Obama's national healthcare program signed up more than 7 million people by the end of March, the president said on Tuesday, notching a rare victory after a months-long, glitch-filled rollout of the law.
Appearing in the White House Rose Garden, the president said 7.1 million people had signed up for coverage under the law, known as Obamacare, and called for Republicans to end their bid to repeal it. House of Representatives Speaker John Boehner repeated his pledge to repeal the law on Monday.
"This law is doing what it's supposed to do. It's working," Obama said, with Vice President Joe Biden standing at his side. "The debate over repealing this law is over. The Affordable Care Act is here to stay."
His remarks represented a victory lap for the administration, which suffered from the botched unveiling of the program's primary website, HealthCare.gov, and wavering support from Americans some three years after the U.S. Congress passed the healthcare law over Republican objections.
Health and Human Services Secretary Kathleen Sebelius, who has taken the brunt of the criticism for the shaky rollout, sat beaming in the front row during the Rose Garden ceremony. White House chief of staff Denis McDonough gave her a hug before Obama's remarks.
Experts had predicted a last-minute surge in enrollment. The figure could give a boost to Democrats, who have suffered from the criticism of the law, ahead of November congressional elections.
Obama's party is seeking to hold on to its control of the U.S. Senate and minimize losses in the Republican-controlled House, but the problems with Obamacare have complicated congressional races and handed Republicans a key talking point for skeptical constituents.
Republicans on Tuesday were quick to highlight outstanding questions including how many of the enrollees had seen their plans canceled because of the new law; how many people saw their premiums go down, and how many people who selected plans actually completed the process and paid their premiums.
"We don't know of course, exactly what they have signed up for, we don't know how many have paid," Senate Minority Leader Mitch McConnell told reporters on Capitol Hill, referring to the enrollees in the program.
"What we do know is that all across the country our constituents are having an unpleasant interaction with Obamacare. Whether they can sign up for a policy or not, they are discovering, of course, higher premiums, a higher deductible."
White House officials dismissed the Republicans' criticism. Speaking to reporters ahead of Obama's announcement, one official noted that Democrats seeking to get voters from the coalition that elected Obama to support them would not be able to do so without embracing the law.
House Democratic leader Nancy Pelosi told reporters her members were not running away from the issue.
"Our members are out there on the offensive on this issue because of what we did, and we're proud of it, and we're proud of what it means in the lives of Americans," Pelosi said after a meeting with Obama.
Monday's deadline for initial enrollment in the program came after a surge in registrations despite the return of technical problems, including a longer-than-expected maintenance session, although nothing as serious as the issues that beset the website's launch in October.
The site on Tuesday announced that open enrollment for Obamacare had closed, but people whose applications were thwarted by technical problems would be given a chance to finish their registration.
By last week, more than 6 million people had signed up for private health coverage through the new Obamacare insurance markets, surpassing a target set after the disastrous rollout called the enrollment process into question.
Industry analysts echoed Republicans' calls for more information about those who had signed up.
"We still have a lot to learn about what underlies those numbers in terms of who signed up and how many were newly insured people versus switching from other coverage," said Karen Pollitz, a senior fellow at the Kaiser Family Foundation.
"We have more to see ... about how many of them actually completed enrollment and how much coverage expansion was accomplished."
The healthcare law, one of Obama's key promises as a presidential candidate in 2008, was intended to expand access to healthcare coverage for millions of uninsured Americans, so having enrollment figures that reflect newly insured people is critical to the program's success.
Having a robust percentage of healthy young people to offset older enrollees is also important. White House spokesman Jay Carney said such details were yet available, but he said the demographic mix would be sufficient to ensure that the health market places that form the cornerstone of the law would function smoothly. (Additional reporting by David Morgan, Thomas Ferraro and Larry Downing; editing by G Crosse)