Governors John Kasich, an Ohio Republican, and John Hickenlooper, a Colorado Democrat, are lobbying their colleagues to support their new plan to stabilize Obamacare.

Kasich and Hickenlooper are looking to the nation's governors for support for their proposal, which they are expected to release this week, before Congress returns Sept. 5 from a month-long recess to begin mapping out their own plan.

Kasich tweeted Monday that the plan is aimed at stabilizing the individual market, which includes Obamacare's exchanges and is used by people who don't have insurance through work.

He said he and Hickenlooper are sharing the ideas with "Republican and Democrat governors in our coalition."

Kasich and Hickenlooper gave some hints last week about what could be in the plan. They told Colorado Public Radio they would like to see changes to Obamacare's employer mandate that demands employers with 50 or more employees provide health insurance.

They also have stoked speculation that they may run in 2020 as a unity ticket. However, both have tried to quash those rumors.

The Senate Health, Education, Labor and Pensions Committee has scheduled hearings Sept. 6 and Sept. 7 on how to stabilize the individual market. Hickenlooper is expected to attend one of the hearings alongside four other governors.

Committee Chairman Sen. Lamar Alexander, R-Tenn., has said he wants to reach a bipartisan deal to stabilize Obamacare's exchanges by the end of September. A likely part of any deal would be funding cost-sharing reduction payments to insurers for 2018. The payments reimburse insurers for reducing out-of-pocket costs for low-income Obamacare customers.