Sen. Lindsey Graham Lindsey Olin GrahamSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-S.C.) said Wednesday he is working on a new version of his ObamaCare repeal-and-replace bill and has not given up on efforts to do away with the law despite Republicans’ failure last year.

“I haven’t given up,” Graham said. “Will there be another effort to replace ObamaCare with a state-centric plan? I hope so.”

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The effort appears to have little, if any, chance of passing this year. Republican leadership has made clear that it has moved on from the ObamaCare repeal effort, and the GOP has an even slimmer margin in the Senate than they did last year when they failed to win enough votes for a bill.

The new bill would keep the core element of last year’s bill from Graham and Sen. 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.), which is repealing ObamaCare’s subsidies and Medicaid expansion and giving that money to the states in a block grant.

The Hill obtained a draft of a revised ObamaCare repeal bill with block grants that Graham and Cassidy worked on earlier this year, though it is not the latest version.

A spokesman for Graham said he had “nothing to add” when asked about the draft.

A spokesman for Cassidy said, “This is a very old draft from about half a year ago that is no longer relevant to Dr. Cassidy’s talks with many senators about new ideas for making health care affordable again. No legislation is imminent.”

Graham said Wednesday that he has been talking to other senators about his effort. “We’re talking to everybody,” he said.

Graham’s effort is working in parallel with an effort from conservative groups like the Heritage Foundation and the Galen Institute, which are working with former Sen. Rick Santorum (R-Pa.) and other groups on a new ObamaCare replacement plan.

The White House told The Hill earlier this month that it “fully supports” the effort, and White House staff have been attending meetings on the plan at the Heritage Foundation.

Santorum was in the Capitol on Wednesday and told The Hill that he had a meeting on the ObamaCare repeal effort earlier in the day.

Graham said Wednesday that he had not spoken to Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Senate GOP aims to confirm Trump court pick by Oct. 29: report Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Ky.) about his effort yet.

“No, I'm just trying to get a product together,” Graham said.