CHICAGO — Today’s deadline for signing up for insurance under the new health care law has 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.