Sens. Lindsey Graham Lindsey Olin GrahamMcConnell locks down key GOP votes in Supreme Court fight Will Republicans' rank hypocrisy hinder their rush to replace Ginsburg? Momentum growing among Republicans for Supreme Court vote before Election Day MORE (R-S.C.) and Bill Cassidy William (Bill) Morgan CassidyCoushatta tribe begins long road to recovery after Hurricane Laura Senators offer disaster tax relief bill Bottom line MORE (R-La.) say they are working to make changes to a bipartisan health-care deal to make it more likely to win favor in the House.

Graham and Cassidy, authors of a failed bill to repeal and replace ObamaCare earlier this year, are supporting a bipartisan measure aimed at stabilizing ObamaCare, but they are also looking for changes to move the proposal to the right.

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They are working with Sen. Ron Johnson Ronald (Ron) Harold JohnsonGOP set to release controversial Biden report Democrats fear Russia interference could spoil bid to retake Senate The Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill MORE (R-Wis.), who has been pushing for changes to the bipartisan bill that would move the bill to the right and possibly make it more palatable to the more conservative House GOP.

Graham and Cassidy said they supported the bipartisan measure from Sens. Lamar Alexander Andrew (Lamar) Lamar AlexanderMcConnell locks down key GOP votes in Supreme Court fight Alexander backs vote on Trump Supreme Court nominee: What Democrats 'would do if the shoe were on the other foot' Toobin: McConnell engaging in 'greatest act of hypocrisy in American political history' with Ginsburg replacement vote MORE (R-Tenn.) and Patty Murray Patricia (Patty) Lynn MurrayTrump health officials grilled over reports of politics in COVID-19 response CDC director pushes back on Caputo claim of 'resistance unit' at agency The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Wash.) but "we recognize this short-term stabilization will not pass unless concerns of the House are addressed."

“We are working with Senator Johnson and House members to include more flexibility provisions like the ones found in our legislation, Graham-Cassidy-Heller-Johnson," Graham and Cassidy said in a joint statement.

Johnson has previously said that the changes he is pushing for include conservative changes like increasing the duration of short-term health insurance plans, expanding health savings accounts, not enforcing the mandate for employers to provide coverage and waiving the penalty under the individual insurance mandate for not having coverage in 2017.