A conservative group founded by ex-Sen. Jim DeMint (R-S.C.) has launched a media campaign in Kentucky to pressure Senate Majority Leader Mitch McConnellMitch McConnellFive things to watch in round 2 of Trump confirmation fights This week: Confirmation fights dominate ahead of inauguration Juan Williams: Race, Obama and Trump MORE (R-Ky.) to back an effort to threaten a government shutdown over defunding ObamaCare.

The Senate Conservatives Fund said it wants McConnell to “feel the heat” over the issue, which has divided Republicans.

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McConnell this week said shutting down the government would not stop the healthcare law. He also said that certain parts of the healthcare law are “probably OK.”

The conservative group accused the GOP leader of “waving the white flag” and blamed him for the fact that other senators were not backing Sen. Mike LeeMike LeeRight renews push for term limits as Trump takes power Conservatives press Trump on Supreme Court pick Overnight Finance: Ethics chief blasts Trump business plan | Senate begins late-night marathon vote | Lawmakers look to rein in Trump on trade MORE’s (R-Utah) effort to move a government-funding measure that defunds ObamaCare.

“Mitch McConnell says some parts of Obamacare are ‘okay.’ Since Mitch McConnell is unwilling to see the light on this issue, we need to make him feel the heat,” an email from the group seeking funds for its campaign reads.

It says it wants to “expose McConnell’s record on this issue and to persuade him to lead the fight.” Many Republicans think Senate Democrats and President Obama will block any government-funding measure that excludes funds for the healthcare law, setting up a scenario where the government would shutdown and Republicans could be blamed.

But the issue continues to have momentum with the grassroots, and could pose a dilemma for McConnell, who faces reelection next year and is being challenged on the right by Marc Bevin in a GOP primary. Bevin has repeatedly accused McConnell of not being aggressive enough in challenging the president’s healthcare law.

DeMint retired from the Senate last year and now heads the Heritage Foundation.