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 McConnell (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.

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 Lee’s (R-Utah) effort to move a government-funding measure that defunds ObamaCare.