Republican Gov. John Kasich of Ohio and Democrat Gov. John Hickenlooper of Colorado on Thursday unveiled a plan to fix Obamacare's exchanges that includes injecting new funds into the controversial law.

The plan calls for Congress to create a temporary stability fund that states can use for a reinsurance program, which reimburses insurers for major losses.

The governors don't give an exact figure for the stability fund. But they pointed to a recent failed Obamacare repeal bill that would have given states $15 billion a year to address issues in Obamacare's individual marketplaces.

"We recommend funding the program for at least two years and fully offsetting the cost so it does not add to the deficit," according to the letter outlining the plan. The letter was sent a week before Congress returns and starts work on a bipartisan stabilization plan.

The Kasich-Hickenlooper plan also aims to boost rural insurer competition by exempting the health insurance tax for any insurer that offers plans in counties that have only one carrier. It would allow residents to buy into the Federal Employee Benefit Program, which gives rural residents the same healthcare access that federal workers get.

"While these proposals may be temporary solutions, they will help provide Americans with additional choices until other policies have improved the market dynamics," the letter said.

The plan calls for strengthening risk adjustment, a program that forces insurers with lower-risk enrollees to send payments to insurers with higher-risk customers. The program has been heavily criticized by smaller insurers who say that it disproportionately charges them too much.

Additionally, the plan seeks to give states more flexibility in selecting essential health benefits, a series of conditions such as hospitalization and mental health coverage that Obamacare plans now have to cover.

The governors want the federal government to pay cost-sharing reduction payments to insurers that reimburse them for lowering copays and deductibles for low-income Obamacare customers. The insurance industry has clamored for a commitment from the White House to make the payments in 2018, and some independent estimates say Obamacare rates could go up an additional 19 percent if they aren't made next year.

The Senate Health, Education, Labor and Pensions Committee is taking the lead in putting together a stabilization package. The panel is holding several hearings next week, and Chairman Sen. Lamar Alexander, R-Tenn., has said he wants to put together a stabilization package by the end of September.

It remains unclear if reinsurance would be included in that package, although payments for the CSRs for 2018 is likely to be included.

Republicans are meeting resistance from conservative groups to a stabilization plan, which many groups have labeled as a bailout for Obamacare.

Republican Gov. Brian Sandoval of Nevada, Independent Gov. Bill Walker of Alaska, and Democratic Govs. Tom Wolf of Pennsylvania, Terry McAuliffe of Virginia, John Bel Edwards of Louisiana, and Steve Bullock of Montana signed on to the letter.