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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 Olin GrahamDurbin: I had 'nothing to do' with Curbelo snub Republicans jockey for position on immigration Overnight Health Care: House passes 20-week abortion ban | GOP gives ground over ObamaCare fix | Price exit sets off speculation over replacement MORE (R-S.C.) and Richard BurrRichard Mauze BurrTrump: Why isn't Senate looking into 'Fake News Networks'? Overnight Cybersecurity: Equifax security employee left after breach | Lawmakers float bill to reform warrantless surveillance | Intel leaders keeping collusion probe open Special counsel looking into dossier as part of Russia probe: report 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 LeeMichael (Mike) Shumway LeeWhatever you think the Alabama special election means, you’re probably wrong How the effort to replace ObamaCare failed Overnight Regulation: Trump temporarily lifts Jones Act for Puerto Rico | Bill would exempt some banks from Dodd-Frank | Senators unveil driverless car bill 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 AlexanderChildren’s health-care bill faces new obstacles Overnight Health Care: Schumer calls for tying ObamaCare fix to children's health insurance | Puerto Rico's water woes worsen | Dems plead for nursing home residents' right to sue Schumer calls for attaching ObamaCare fix to children's health insurance 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.