Last-minute insurance shoppers given grace period Updated: Tuesday, December 24, 2013 | CHICAGO (AP) - Federal officials are still encouraging people to sign up for health insurance by the end of today, if possible, instead of waiting until tomorrow. But Americans are getting that extra day to do so, and still get coverage by the first of January. The deadline was extended because of concerns that there would be heavy traffic today on the government's health care website. The federal HealthCare.gov system serves 36 states. Some other states have also extended enrollment deadlines slightly.