MONTPELIER -- Gov. Peter Shumlin on Thursday encouraged people who are eligible for health insurance through the Vermont Health Connect system to sign up by Dec. 23, the deadline to receive a federal subsidy and have coverage effective Jan. 1.

Shumlin said the problems that plagued the state's health care website after its Oct. 1 launch are diminishing and residents are signing up in increasing numbers. About 45,000 of the 65,000 people the state estimates qualify for health insurance coverage through the federally mandated health insurance exchanges have signed up, the governor said at a Statehouse news conference.

About 5,000 people have signed up since Monday, Shumlin said.

"We've signed up in the last four or five days as many people as signed up in the first five to six weeks of Vermont Health Connect," he said.

The governor and other officials encouraged residents to sign up, noting it could be done through the website, by phone or through a one-on-one session with a trained "navigator."

Shumlin has said consistently he's been frustrated by efforts to get the system working and ensure people keep their health insurance coverage. The state made a number of changes after the troubles with the website became apparent, including allowing Vermonters to extend their current policies through March 31. Small businesses can now go directly to the state's two health insurance providers, Blue Cross Blue Shield of Vermont and MVP Healthcare, to arrange coverage.

"It's important for us to remember in light of the fact that on October 1st we didn't get off to the start that we wished we had," Shumlin said. "We've got to keep our eye on the prize. And the prize is there are too many Vermonters who wake up every morning knowing that if they really get sick, if they really need health care, they have to make awful choices in order to get that health care because they can't afford it."

The federal health care website similarly had a troubled rollout.

State Sen. Claire Ayer, D-Addison, the chairwoman of the Senate Health and Welfare Committee, and state Rep. Mike Fisher, chairman of the House Health Care Committee, both said they'd been to events where people seeking insurance had been working with the so-called navigators, who are trained to help individuals sign up.

Fished said he'd spoken with a person who signed up and was pleased to learn he was saving a significant amount of money under the new system.

"I also have had the experience in the last couple of weeks where people have actually crossed the street to come and grab me by the arm and say, ‘I know you're hearing a lot of grief, I know that there are a lot of bad stories out there, but I want you to know I signed up and it wasn't as bad as people were saying,'" Fisher said. "That's the recent story."