ST. PAUL — Enrollment in Minnesota’s struggling online health insurance exchange has grown to more than 53,000 people as a critical sign-up deadline nears, MNsure’s board of directors was told Monday.

The number of Minnesotans who have chosen a plan and a payment method as of Friday is up about 14,000 more from mid-December, when the total was nearly 39,000. The total includes people obtaining private insurance as well as coverage through the state-run MinnesotaCare and Medical Assistance programs for lower-income people.

Tuesday at midnight is the deadline for Minnesotans to choose a plan and enroll through MNsure to get coverage that takes effect on New Year’s Day. The deadline was pushed back from Dec. 23 to accommodate consumers struggling to navigate the clunky website. For those still having trouble with the website, the deadline for paper applications is 6 p.m. Tuesday.

People who sign up by Tuesday have until Jan. 10 to pay their first month’s premium. Those who miss the Tuesday deadline have until the end of March to pick a plan before facing penalties, but won’t be covered until they do.

MNsure has seen a “steady growth in coverage” but still has technical problems that need to be overcome, Interim CEO Scott Leitz told the board. He also said people who know they absolutely must have coverage in place by Wednesday should consider buying it directly from an insurance company.

“While progress is being made, I think it is safe to say there’s still more that needs to be done. … Not everyone is having a perfect experience yet,” said Leitz, a former assistant state human services commissioner. Leitz got the job Dec. 18 after the abrupt resignation of April Todd-Malmlov, who led the drive to build MNsure but came under fire for ongoing troubles with its rollout and for taking a two-week tropical vacation while they remained unsolved.