The 7 million target, thought to be out of reach by most experts, was in sight on a day that saw surging consumer interest as well as vexing computer glitches that slowed sign-ups on the HealthCare.gov website.
Two government officials confirmed the milestone, speaking on condition of anonymity because they were not authorized to discuss the matter ahead of an official announcement.
Seven million was the original target set by the Congressional Budget Office for enrollment in taxpayer-subsidized private health insurance through new online markets created under Obama's signature legislation.
That was scaled back to 6 million after the disastrous launch of HealthCare.gov last fall. Several state-run websites also had crippling problems.
Americans who rushed to apply for health insurance Monday faced long, frustrating waits and a new spate of website ills on deadline day.
"This is like trying to find a parking spot at Wal-Mart on Dec. 23," said Jason Stevenson, working with a Utah nonprofit group helping people enroll.
At times, more than 125,000 people were simultaneously using HealthCare.gov, straining it beyond its capacity. For long stretches Monday, applicants were shuttled to a virtual waiting room where they could leave an email address and be contacted later.
Officials said the site had not crashed but was experiencing very heavy volume. The website, which was receiving 1.5 million visitors a day last week, had recorded about 2 million through 3 p.m. EDT. Call centers have more than 840,000 calls.
Supporters of the health care law fanned out across the country in a final dash to sign up uninsured Americans. People not signed up for health insurance by the deadline, either through their jobs or on their own, were subject to being fined by the IRS, and that threat was helping drive the final dash.
The administration announced last week that people still in line by midnight would get extra time to enroll.
The website stumbled early in the day - out of service for nearly four hours as technicians patched a software bug. Another hiccup in early afternoon temporarily kept new applicants from signing up, and then things slowed further. Overwhelmed by computer problems when launched last fall, the system has been working much better in recent months, but independent testers say it still runs slowly.
At Chicago's Norwegian American Hospital, people began lining up shortly after 7 a.m. to get help signing up for subsidized private health insurance.
Lucy Martinez, an unemployed single mother of two boys, said she'd previously tried to enroll at a clinic in another part of the city but there was always a problem. She'd wait and wait and they wouldn't call her name, or they would ask her for paperwork that she was told earlier she didn't need, she said. Her diabetic mother would start sweating so they'd have to leave.
She's heard "that this would be better here," said Martinez, adding that her mother successfully signed up Sunday at a different location.
At St. Francis Hospital in Wilmington, Del., enrollment counselor Hubert Worthen plunged into a long day. "I got my energy drink," he said. "This is epic, man."
At a Houston community center, there were immigrants from Ethiopia, Nepal, Eritrea, Somalia, Iraq, Iran and other conflict-torn areas, many of them trying anew after failing to complete applications previously. In addition to needing help with the actual enrollment, they needed to wait for interpreters. Many had taken a day off from work, hoping to meet the deadline.
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.
New York, running its own site, reported more than 812,000 had signed up by Sunday morning, nearly 100,000 of them last week.
However, it's unclear what those numbers may mean.
The administration hasn't said how many of the 6 million people nationally who had signed up before the weekend ultimately closed the deal by paying their first month's premiums. Also unknown is how many were previously uninsured - the real test of Obama's health care overhaul. In addition, the law expands coverage for low-income people through Medicaid, but only about half the states have agreed to implement that option.
Cheering on the deadline-day sign-up effort, Health and Human Services Secretary Kathleen Sebelius planned to spend much of the day Monday working out of the department's TV studio, conducting interviews by satellite with stations around the country.
Though March 31 was the last day officially to sign up, millions of people are potentially eligible for extensions granted by the administration.
Those include people who had begun enrolling by the deadline but didn't finish, perhaps because of errors, missing information or website glitches. The government says it will accept paper applications until April 7 and take as much time as necessary to handle unfinished cases on HealthCare.gov. Rules may vary in states running their own insurance marketplaces.
The administration is also offering special extensions to make up for all sorts of problems that might have kept people from getting enrolled on time: Natural disasters. Domestic abuse. Website malfunctions. Errors by insurance companies. Mistakes by application counselors.
To seek a special enrollment period, contact the federal call center, at 1-855-889-4325, or the state marketplace and explain what happened. It's on the honor system. If the extension is approved, that brings another 60 days to enroll.
Those who still don't get health insurance run the risk that the Internal Revenue Service will fine them next year for remaining uninsured. It remains to be seen how aggressively the penalties called for in the law are enforced.
Also, the new markets don't have a monopoly on health insurance. People not already covered by an employer or a government program can comply with the insurance mandate by buying a policy directly from an insurer. They'll just have to pay the full premium themselves, although in a few states there may be an exception to that rule as well.
Supporters of the law held their breath early Monday when the website was taken down.
In Oakton, Va., enrollment counselor Rachel Klein said she noticed the website was running slowly.
"We all came into it understanding that today was going to be challenging," said Klein. "We're all relieved that there's going to be a little extra time for people."
House Speaker John Boehner of Ohio said Monday that Republicans remain committed to repealing Obama's law.
Associated Press writers Connie Cass in Washington, Don Babwin in Chicago, Randall Chase in Wilmington, Del., Ramit Plushnick-Masti in Houston, Michelle Price in Salt Lake City and Carolyn Thompson in Buffalo, N.Y., contributed to this report.