CHICAGO — Anticipating heavy traffic on the government’s health care website, the Obama administration extended Monday’s deadline for signing up for insurance by a day, giving Americans in 36 states more time to select a plan.

Julie Bataille, a spokesman for the federal agency in charge of the overhaul, said the grace period — which runs through today — was being offered to accommodate people from different time zones and to allow for any technical problems that might result from a last-minute rush of applicants.

The HealthCare.gov site has gone through extensive improvements to make it more reliable and increase its capacity, and the administration said the system was running well Monday.

By the afternoon, the site had received a record 850,000 visits, five times the number logged by the same time last Monday, the administration said.

Bataille said the system was handling the volume with error rates of less than 1 in 200 and response times of less than one second.

The Obama administration is hoping for a surge of year-end enrollments to show that the technical problems were merely a temporary setback. That would also go a long way toward easing concerns that insurance companies won’t be able to sign up enough young, healthy people to keep prices low for everyone.

Monday had been the deadline for Americans in the 36 states served by the federal site to sign up if they wanted coverage at the start of the new year. The remaining states operate their own online marketplaces, and some of them have also extended their deadlines.

As the deadline drew near, more than 1 million people visited the website over the weekend, and a federal call center received more than 200,000 calls.