Sen. Jim DeMint (R-S.C.) introduced legislation to finish what the House started, and repeal President Obama's signature healthcare reform.

DeMint, joined by 35 Republican co-sponsors, introduced a bill mirroring House legislation passed last week to do away with the reform law.

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The DeMint legislation allows GOP senators to put themselves on the record about their support for repeal, via their sponsorship of the DeMint bill in the Senate.

"Republicans are standing with the American people who are demanding we repeal this government takeover of health care,” DeMint said in a statement. “Repealing ObamaCare is vital to the future of our nation and the health of our people.

Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellJudiciary Committee greenlights Garland's AG nomination This week: Senate takes up coronavirus relief after minimum wage setback Juan Williams: Hypocrisy runs riot in GOP MORE (R-Ky.) has said he'll "assure" a Senate vote on repeal, and on Tuesday night made a procedural move to add the House-passed repeal bill to the Senate calendar.

"It's a vote we ought to have. It's very high on the agenda of the American people. We'll have the vote one way or the other," the top Senate Republican said of that bill on MSNBC.

Eleven Senate Republicans had not yet signed on as co-sponsors, though they could add their name to that list in the future. Four of them — Sens. Lamar AlexanderLamar AlexanderCongress addressed surprise medical bills, but the issue is not resolved Trump renominates Judy Shelton in last-ditch bid to reshape Fed Senate swears-in six new lawmakers as 117th Congress convenes MORE (Tenn.), Richard Lugar (Ind.), Lisa MurkowskiLisa Ann MurkowskiMurkowski says no decision after Tanden meeting Green New Deal's 3 billion ton problem: sourcing technology metals The Hill's Morning Report - Presented by Facebook - Trump teases on 2024 run MORE (Alaska) and Jeff SessionsJefferson (Jeff) Beauregard SessionsManchin flexes muscle in 50-50 Senate Udalls: Haaland criticism motivated 'by something other than her record' Ocasio-Cortez targets Manchin over Haaland confirmation MORE (Ala.) — had previously declined to sign onto McConnell's court brief supporting a constitutional challenge to healthcare reform. 

This post was updated at 1:30 p.m. to reflect that Sen. Scott Brown (R-Mass.) had signed on as a co-sponsor to the bill.