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 McConnellKavanaugh gets questionnaires for confirmation hearing Dem infighting erupts over Supreme Court pick Franken offers Dems a line of questioning for Kavanaugh's 'weirdly specific bit of bulls---' 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 AlexanderAndrew (Lamar) Lamar AlexanderSens introduce bipartisan bill matching Zinke proposed maintenance backlog fix Supreme Court vacancy throws Senate battle into chaos Overnight Health Care: Anti-abortion groups see chance to overturn Roe v. Wade with Kennedy retirement | HHS watchdog to probe detention center conditions | VA pick vows to oppose privatization MORE (Tenn.), Richard Lugar (Ind.), Lisa MurkowskiLisa Ann MurkowskiDem infighting erupts over Supreme Court pick McConnell: Senate to confirm Kavanaugh by Oct. 1 Overnight Energy: House to vote on anti-carbon tax measure | Dem says EPA obstructed 'politically charged' FOIA requests | GOP looks to overhaul endangered species law MORE (Alaska) and Jeff SessionsJefferson (Jeff) Beauregard SessionsConservatives moving to impeach Rosenstein soon: report Senators urge DOJ to probe whether Russians posed as Islamic extremist hackers to harass US military families The Hill's Morning Report — Trump readies for Putin summit: 'He’s not my enemy’ 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.