ST. PAUL — After two years of vilifying the federal health overhaul and the state’s health insurance exchange, Minnesota Republicans face Democratic opposition in the Senate and governor’s office that will scale back their hopes for a wholesale makeover.

Fresh off winning back the state House, Republicans are mapping out their plans to tweak MNsure in 2015. For now, they’re leaving everything on the table: from altering its board to giving lawmakers budgetary control of the independent entity.

Top Democrats in the House and Senate have signaled they’re open to shaking up MNsure’s seven-member board. Republicans have repeatedly called for a county official and health insurance company representative to take a spot.

But Republicans may mix in more audacious proposals that would likely be non-starters for Democrats.

That could even include pursuing a wholesale repeal as the GOP looks to 2016 and future elections.

“It has to be clear that Republicans and Democrats can work together to do what’s right for Minnesota,” said GOP Sen. Michelle Benson, a longtime MNsure critic. “But Republicans also have to be very clear about what we would do differently moving forward.”

With Gov. Dayton’s re-election and the state Senate in Democrats’ control until at least 2016, House Republicans acknowledge abolishing the state’s exchange is farfetched. But that doesn’t mean they won’t talk about it.

“Ultimately, I think we’d like to,” incoming House Speaker Kurt Daudt said of repeal. “We want to be realistic on what we can accomplish.”

They’ll also have to contend with the legal reality of satisfying the Affordable Care Act.

While those larger questions simmer, Republican lawmakers say there are easier fixes to address MNsure’s troubled rollout last year. Chief among them: new board members.

Rep. Tara Mack, an Apple Valley Republican who will chair the Health and Human Services Reform committee, said it was a mistake not to put a county representative on MNsure’s board. As the exchange faltered last year, counties manually processed thousands of applications for public health programs like Medicaid.

Rep. Joe Atkins and Sen. Tony Lourey, the Democrats who sponsored bills that created the exchange, said they’d be open to the change. But Atkins said he worried about installing a health insurance representative on the board, citing possible conflict of interest.