ST. PAUL— Lackluster enrollment in private plans and drying-up federal funds may force Minnesota to pick up more of the tab for its health insurance exchange.

MNsure would get another $11.7 million of state money under Gov. Mark Dayton’s proposed budget for technological improvements — a necessary change because public-plan signups have far outpaced private-plan enrollments.

The governor is also recommending the state assume costs the federal government covered until this year, such as $1.3 million over the next two years for staff to review rate submissions from insurance companies and another $558,000 to investigate complaints. Most federal funding has expired as Washington’s aim is to make state-run health exchanges self-sufficient.

Together, those changes would bring the state’s running costs for the exchange to at least $23.5 million since it was set up in 2013.

Republicans say the state chipping in more money proves their point that the exchange isn’t sustainable and needs drastic change.

“It’s not a surprise that’s happening, but it’s a hidden cost,” said Sen. Michelle Benson, a Ham Lake Republican.

House Republicans grilled officials from MNsure and other state agencies Thursday, pressing for details about how those additional funds would be spent on the struggling website.

“Will that fix the problems?” asked Rep. Joe McDonald, R-Delano.

Lawmakers set up MNsure mostly with federal funds, aiming to sign up Minnesota residents in both private plans and public programs for lower-income families like MinnesotaCare and Medical Assistance.