The director of Minnesota’s health insurance exchange, April Todd-Malmlov, abruptly resigned this week, making the exchange the fourth state program to see a leadership change in the midst of mounting criticism over the rollout of President Obama’s new health care law.

At a news conference on Wednesday, Ms. Todd-Malmlov’s successor was quick to promise fixes to problems still plaguing consumers, many of whom are worried about getting coverage by Jan. 1, when new policies under the law are set to take effect.

“There is no doubt that this process will improve moving forward,” said Scott Leitz, who was named the interim chief executive of MNsure, Minnesota’s state-run marketplace. “It will be a much better process than it is now, and it will be much easier to enroll.”

Ms. Todd-Malmlov had been in damage-control mode for weeks, but calls for her removal grew after she took a tropical vacation in November — a trip seen as politically unwise at a moment of crisis for the fledgling marketplace, while frustrated residents encountered issues with the website and call center.