ST. PAUL — Minnesotans who want new health insurance on Jan. 1 have a week to buy policies through the state-run MNsure program, but problems continue to surface as that deadline nears.

On Monday, for instance, people wanting to sign up on the MNsure website were greeted with: “We are currently experiencing issues with new applications requesting 1/1/14 plan coverage. We are working to resolve this issue.”

MNsure spokeswoman Jenni Bowring-McDonough said she did not know the problem’s cause.

She said that anyone who signs up and pays for insurance by Dec. 23 will have coverage Jan. 1.

The Web issue is one of a number of problems that plague MNsure, issues ranging from nearly hourlong waits to getting anyone to answer the MNsure telephone to its director taking a two-week Costa Rica vacation last month during what Gov. Mark Dayton called a critical time for the insurance-sales agency.

“It’s up to the governor now,” House Minority Leader Kurt Daudt, R-Crown, said as he and Senate Minority Leader David Hann, R-Eden Prairie, urged Democrat Dayton to fix the problems.

MNsure is a separate agency and the governor has no direct control over it, but Daudt and Hann said Dayton is the one who must take action.

Fellow Republican Scott Hounor, a governor candidate, said there is nothing Dayton can do. Honour was especially upset about the executive director’s Costa Rica trip last month.