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 McConnellMitch McConnellGOP senators: House agreeing to go to conference on ObamaCare repeal Ryan drops border-tax proposal as GOP unifies around principles Pence raises million for PAC at fundraiser: report 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 AlexanderOvernight Healthcare: Senate rejects repeal-only ObamaCare plan | Ads target Heller, Capito over vote | Dem says ObamaCare repeal effort moving US 'toward single-payer' Senate rejects repeal-only ObamaCare plan Senate delays vote on healthcare repeal MORE (Tenn.), Richard Lugar (Ind.), Lisa MurkowskiLisa MurkowskiOvernight Regulation: Driverless car bill moves quickly to House floor | Dems grill Trump bank regulator nominees | Halliburton to pay .2M to settle SEC violation Overnight Energy: Zinke jumps into ObamaCare fight | States threaten to sue EPA Key senator backs 'skinny' ObamaCare repeal MORE (Alaska) and Jeff SessionsJeff SessionsSessions says he doesn't regret recusing himself from Russia probe NY Post cover depicts Trump White House as reality TV show 'Survivor' Trump to announce MS-13 gang crackdown in Long Island 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.