CHICAGO » Today’s deadline for signing up for insurance under the new health care law has effectively been extended through Tuesday in case of heavy demand on the government website.

Julie Bataille, a spokeswoman for the federal agency overseeing the Obama administration’s health overhaul, says the grace period is being offered to accommodate people from different time zones and to deal with potential technical problems that could result from a last-minute rush of applicants.

Today was the deadline for Americans who wanted coverage that started on Jan. 1.

The federal HealthCare.gov system serves 36 states. Some other states have also extended enrollment deadlines slightly.

With the deadline looming, more than 1 million people visited the refurbished federal enrollment website over the weekend, and a federal call center received more than 200,000 calls. Thirty-six states rely on the federal website for enrollment.

The original deadline was pushed back a week because of the technical problems that plagued the federal marketplace for weeks after its October opening, but hundreds of upgrades to storage capacity and software have cut error rates and wait times.

"It’s just nonstop now. Everybody knows about it. Everybody wants it," said Florida enrollment counselor Madeleine Siegal. She said her organization in Fort Lauderdale was slammed with walk-ins and appointments Friday, had several weekend enrollment events and planned to open its doors earlier than usual today.

Ronald Bellingeri, a 59-year-old general contractor in Florida, signed up Friday in 90 minutes with help from an enrollment counselor. Bellingeri said he waited until the last minute because he didn’t know what to do or where to go.

On Friday, he chose a gold plan with a $156 monthly premium. The government is picking up $472 per month because of his income.

"I just walk in the door and an hour and a half later, I have health insurance. It makes me feel great," he said.

Others said they will let the date pass without making a decision.

"I’m in no hurry, though it’d be nice to be able to visit a doctor without stress," said Kyle Eichenberger, an uninsured 34-year-old from Oak Park, Ill.

Eichenberger said he hit a wall on the website when he first tried to enroll. More recently, the 34-year-old stay-at-home dad hasn’t had time to get his questions answered. His family situation doesn’t fit into a neat category: His children and their mother have health insurance through her job. But her employer doesn’t offer coverage to opposite-sex domestic partners, and the couple are not married.

"I’m an Obamacare supporter, though I think it is full of problems," Eichenberger said. "It’s better than the system we had before and already helps my kids get free preventive care. I’d like to see the whole system streamlined to be more user-friendly. Keep the basic idea, but don’t make me feel like I’m navigating a maze to get a simple checkup."

Minnesota, one of the states running their own insurance exchanges, had long planned a deadline today to sign up for coverage starting Jan. 1. But amid problems with its website and extra-long hold times to reach its help center, the state last week postponed the deadline by eight days, letting people sign up through Dec. 31.

Maryland has also extended its deadline, to Dec. 27.

In Washington state, people who got up early today to start their application for health insurance on the state’s online marketplace may have been disappointed. The site was down for maintenance until nearly 9 a.m.