WASHINGTON — More than 7 million Americans have now enrolled in private coverage on the nation’s health insurance marketplaces, thanks to a wave of late sign-ups that pushed the enrollment tally beyond the original goal set by the Congressional Budget Office.A fiery President Barack Obama made the formal announcement in a Rose Garden ceremony Tuesday that served as a victory lap and pep rally for administration officials, Democratic lawmakers and civilian volunteers who labored in support of the health law despite a flawed federal enrollment website, a skeptical public and stiff opposition from Republicans.While further challenges remain, both politically and logistically, the unexpected success of the marketplace enrollment period helps ensure that the president’s signature legislation will usher in one of the broadest expansions of national health coverage since Medicaid and Medicare were launched in 1965 and the Children’s Health Insurance Program was established in 1997.Through a combination of new marketplace insurance, coverage for people up to age 26 on their parents’ health plans and expanded Medicaid eligibility, 9.5 million to 9.8 million uninsured Americans have likely gained health coverage under the law, said economist Katherine Carman of the RAND Corp., a nonprofit think tank in Santa Monica, Calif.Obama told the Rose Garden gathering: “The Affordable Care Act hasn’t completely fixed our long-broken healthcare system. But this law has made our healthcare system a lot better — a lot better.“Citizens know the economic security of health insurance who didn’t just a few years ago,” the president said. “And that’s something to be proud of. Regardless of your politics or your feelings about me or your feelings about this law, that’s something that’s good for our economy. That’s good for our country. And there’s no good reason to go back.”His tone and demeanor were in sharp contrast to the dejection and frustration he showed in a November White House speech when the HealthCare.gov website was broken and he was compelled to let people with canceled health plans keep their coverage for another year.On Tuesday, he exuded confidence about the health law’s future, as well as irritation and amazement over the constant political attacks that it continues to endure.“I’ve got to admit: I don’t get it,” he said. “Why are folks working so hard for people not to have health insurance? Why are they so mad about the idea of folks having health insurance? Many of the tall tales that have been told about this law have been debunked. There are still no death panels. Armageddon has not arrived. Instead, this law is helping millions of Americans, and in the coming years it will help millions more.”The enrollment milestone is the payoff of a lean but resourceful operation that deployed tools, tactics and metrics honed on the campaign trail to enroll as many people as possible over the last six weeks, according to senior administration officials.The hope was to reach young people, minorities and moms, with special focus on states like Texas, Florida, Georgia and North Carolina with high rates of uninsured, and 25 cities with similarly high rates.Republicans were unmoved by the numbers, noting that the White House still hasn’t answered questions about the enrollees, including how many have actually paid their premiums.House Republicans said the figures don’t affect the pledge this week of House Speaker John Boehner, R-Ohio, to continue trying to repeal the law.