MINNEAPOLIS — Minnesotans who make a good faith effort to enroll for coverage through the state’s new health insurance exchange by the March 31 deadline will get a reprieve if they run into problems and cannot complete the process, officials said Monday.

MNsure chief Scott Leitz compared the situation to people who are still waiting in line when polls close on election day: They still get to vote. So those who are still “in line” when the enrollment deadline hits at 11:59 p.m. CDT on March 31 will still be able to get insurance coverage and avoid the tax penalty, he told reporters on a conference call.

Consumers can fill out an “enrollment attempt” form on the MNsure website or call the exchange’s call center to establish that they made a good faith but unsuccessful effort to sign up, said Katie Burns, policy and plan management director. But the exchange will accept other documentation, too, including having opened an account within the MNsure system; paper applications submitted to a government agency, navigator or broker records; call center records; emails sent to MNsure; and documents filed in appeals.

MNsure officials will then work with consumers and the insurance companies to resolve the holdups, Burns said.

Leitz said he did not know how many people might take advantage of the reprieve, but said they’re expected to include procrastinators who have not tried to sign up yet, as well as people who have tried but have not been able to complete the process due to technical glitches or other snags. MNsure’s trouble-plagued website is “functioning well” now, he said. The number of people whose applications remain stuck in the system is “relatively small” and MNsure officials are actively working with them, he said.

Gov. Mark Dayton issued a statement expressing “strong support” for the extension.

More than 130,000 people had signed up for coverage through MNsure as of Friday. The exchange has a goal of 135,000 and plans to issue updated enrollment figures Tuesday.