The first yearly sign-up period for Obamacare closes today, with early returns suggesting the administration may reach a projection of 7 million enrollees made before the U.S. health exchange struggled at its startup.

The rollout has been under constant attack from Republican foes and faced a key U.S. Supreme Court decision that allowed states to limit the Medicaid expansion that was an important part of the plan. It also suffered from myriad technical flaws in the website that made it unusable for more than a month.

The government last week said 6 million Americans had enrolled by March 27 and about 1 million people a day were visiting healthcare.gov. The sign-ups met a mark set by the Congressional Budget Office in February that was reduced from an initial 7 million estimate after the law’s troubled start in October. Republicans questioned the credibility of the numbers.

“I think they’re cooking the books on this,” said Senator John Barrasso, a Wyoming Republican, in an appearance yesterday on Fox News Sunday. “What kind of insurance will those people actually have? Will they be able to keep the doctor that they want? How much more is it going to cost them?”

Under the law, enrollment ends at 11:59 p.m. New York time for the 36 states served by the federal government’s exchange. The administration said last week it will accept enrollment from anyone who began the process before the deadline, which means final data may not be available for weeks.

Those who don’t sign up face a fine of as much as 1 percent of their yearly income.

Younger Enrollees

The percentage of younger people who enroll is also important because they’re expected to use fewer medical services than older people. The more young and healthy people insurers cover, the less risk they face, reducing future premium increases.

“The president of WellPoint, which is one of the big national insurance companies, said a couple of weeks ago that the sign-ups are getting younger by the day,” saidnSenator Angus King, a Maine independent. “In other words, younger people, not surprisingly, are the last people to sign up.

‘‘I suspect that’s who is signing up today and tomorrow,’’ King said on Fox News Sunday.

The 6 million figure announced by the administration reflects only people who selected a plan using the exchanges, not those who have paid their first premium to their insurer -- the final step required to complete enrollment.

While Republicans have pressed for that number, U.S. officials have said it isn’t available because a system to automatically transfer data between the government and insurers isn’t finished.

Previously Insured

The government also hasn’t said how many of the 6 million enrolled previously had insurance. Assessing whether the Patient Protection and Affordable Care Act has progressed toward its goal of covering more of the 48 million people who lacked insurance in 2012 depends on that information.

The law provides a number of specific exemptions from the penalty, and the Obama administration has created others, using a broad exception for ‘‘hardships.” People who aren’t eligible for subsidies in the exchanges don’t have to pay the penalty if the lowest insurance premium they can find would cost more than 8 percent of their income.

Hardship exemptions include a death in the family, bankruptcy or foreclosure, victims of domestic violence and people who couldn’t pay medical bills in the past two years.

For those who don’t sign up by today and aren’t eligible for an extension, enrollment opens in November for coverage starting in January 2015.

The administration gave itself a round of applause last week for the achievement, putting Obama on a conference call from Italy to congratulate thousands of volunteers and workers with nonprofit organizations and government agencies who have helped sign people up.

“Join the 6,000,000 Americans who now have health coverage thanks to the Affordable Care Act,” a March 27 e-mail from the Health and Human Services Department said. “Just 4 days left!”

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