Nearly 50,000 Massachusetts residents have signed up for an insurance plan through the state's health connector and made their first month's payment.

Health Care connector officials said as of Sunday night, about 49,900 residents had taken the steps needed to guarantee they have coverage on Jan. 1.

The original enrollment deadline was Dec. 23, but connector officials had given thousands of people who had chosen a plan but not yet paid for until Sunday to do so.

Some people may receive their health plan's ID cards a few days after Jan. 1, but their coverage will be in effect at the start of the month.

Officials say the revamped connector website has been operating without major glitches since it was launched Nov. 15, replacing one that was hobbled by technical problems.