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It's the group's third radio ad hitting incumbent senators over the issue. SCF on Tuesday launched ads targeting Sens. Lindsey GrahamLindsey GrahamGraham: Trump's Charlottesville rhetoric 'dividing Americans, not healing them' OPINION: Congress should censure Trump for his unfit conduct Supporting 'Dreamers' is our civic and moral duty MORE (R-S.C.) and Richard BurrRichard Mauze BurrSenate chairman hopes to wrap up Russia investigation this year Lawmakers seek to interview Trump secretary in Russia probe Senate Dem wants closer look at Russia's fake news operation on Facebook MORE (R-N.C.) for their opposition to a threatened government shutdown over defunding ObamaCare.

The ad targeting Alexander is notable because he's been an outspoken opponent of the law.

The top Republican on the Senate Health, Education, Labor, and Health Committee, Alexander has previously called the law "a historic mistake" and repeatedly voted for its repeal and to delay its implementation.

But he wasn't one of a handful of Republicans to sign onto a letter circulated by Tea Party Sen. Mike LeeMike LeeTrouble draining the swamp? Try returning power to the states Congress must act to protect data privacy before courts make surveillance even easier Five tough decisions for the GOP on healthcare MORE (R-Utah) pledging to oppose a government funding measure, and effectively shut down the government, if the measure doesn't include a provision defunding ObamaCare.

The SCF ad charges that "Republicans in Congress can stop ObamaCare by refusing to fund it, but Senator Lamar AlexanderAndrew (Lamar) Lamar AlexanderTrump to make ObamaCare payments to insurers for August CBO: ObamaCare premiums could rise 20 percent if Trump ends payments CBO to release report Tuesday on ending ObamaCare insurer payments MORE refuses to join the fight."

"Lamar Alexander voted to give President Obama money to implement ObamaCare earlier this year, and he'll do it again if you don't make your voice heard," a narrator ads.

The ad warns that the law is a "job killer" and a "liberal train wreck," and calls for listeners to sign a petition urging Alexander to join the defunding effort. It's backed by a $45,900 buy and will run on Tennessee radio for two weeks beginning Thursday.

Alexander looks well-poised for reelection, but SCF has long criticized the Senator and recently blasted him for his support of the immigration reform law that passed the Senate earlier this year.

He received his first primary challenger in state Rep. Joe Carr, who entered the race this week, but SCF's executive director, Matt Hoskins, indicated the group is unlikely to back him.

“If Carr doesn’t catch fire and a more compelling conservative enters the race, he could be the spoiler that helps re-elect Lamar Alexander. That’s something we want to avoid," he told The Tennessean.

The SCF ad is, however, an indication the group is still watching the race and looking for a stronger challenger.