ST. PAUL  — Minnesota would use state money to offset the health premium hikes for more than 100,000 residents under a measure legislators were considering Thursday, a novel approach as states across the country grapple with the rising costs and uncertain future of the Affordable Care Act.

As the only Midwestern state to create its own insurance marketplace, Minnesota was an early adopter of President Barack Obama’s health care law. However, it faces some of the nation’s largest rate increases this year, driven in part by higher-than-expected medical costs for a small, severely sick population of residents who buy coverage on their own.

Even as President-elect Donald Trump plots a repeal of the law after taking office Friday, Minnesota officials from both parties agree they need to step in and help by tapping roughly $300 million in rainy day funds.

“I urge the Legislature to agree to health insurance premium relief immediately, so that we can get help to the Minnesotans who need it most,” Gov. Mark Dayton said this week.

The state support wouldn’t be available to shoppers who get federal subsidies, instead going to those faced with covering premium increases that range from an average of 50 percent to 67 percent just since last year.

But Dayton and Minnesota’s Republican Legislature haven’t yet agreed on how to structure the relief, or whether it should be paired with broader market changes like ushering for-profit insurance companies into a state that currently bans them. The state House approved its own plan Thursday that would cover 25 percent of a person’s entire monthly premium.

Most states saw double-digit premium increases for 2017, but Minnesota’s response is unique. Alaska answered instability in its individual market by creating a reinsurance program last year to help insurance companies cover unexpected losses.

In Minnesota, the money would go directly to residents like Tracie Loeffler, an adjunct college professor whose family’s monthly bill jumped 62 percent from 2016, along with a new, $10,000 deductible. Their premium payments are now larger than their mortgage.

“We’re burning through our savings just to pay for basic health care, and that’s not right,” she said.

But the debate surrounding how to help residents like Loeffler isn’t over, and it hasn’t been easy. The plans have been in the works since the fall, when the rate increases were first unveiled and Dayton proposed a premium rebate. It was the subject of special session talks that fizzled out before the Minnesota Legislature returned earlier this month.

Dayton and legislative Republicans still need to agree on how they’ll help. Dayton has called to route the money through insurance companies to reduce premiums directly, saying Republicans’ proposal requiring income testing and checks from the state would result in months of delays.

“Minnesotans need our help now,” House Minority Leader Melissa Hortman said Thursday night.

Republican House Speaker Kurt Daudt said he thinks they can nail down an agreement and send relief within the next week.