The Senate Conservatives Fund (SCF) is targeting Sens. Lindsey GrahamLindsey Olin GrahamTop Louisiana health official rips Cassidy over ObamaCare repeal bill Senate Dems hold floor talk-a-thon against latest ObamaCare repeal bill Overnight Defense: Senate passes 0B defense bill | 3,000 US troops heading to Afghanistan | Two more Navy officials fired over ship collisions MORE (R-S.C.) and Richard BurrRichard Mauze BurrLawmakers grapple with warrantless wiretapping program Facebook under fire over Russian ads in election 5 senators call for US to shutter embassy in Havana MORE (R-N.C.) with radio ads blasting their opposition to a threatened government shutdown over defunding ObamaCare.

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The Tea Party-affiliated group's move is a warning to the two senators not to position themselves against the conservative base, and is especially notable since Burr won't face election again until 2016. 

Graham has a trio of 2014 primary challengers, though he appears to be in a strong position for reelection.

"Republicans in Congress can stop ObamaCare by refusing to fund it, but Senator Richard Burr says that's 'the dumbest idea he's ever heard.' Really? What's dumb is for Richard Burr to vote to fund a government program like ObamaCare that will do so much harm to North Carolina families," the ad's narrator says in the North Carolina ad.

A similar ad is running against Graham criticizing him for calling the plan "a bridge too far."

The move is the latest salvo in a fight between hardline conservatives led by Sen. Mike LeeMichael (Mike) Shumway LeeOvernight Defense: Senate passes 0B defense bill | 3,000 US troops heading to Afghanistan | Two more Navy officials fired over ship collisions Senate passes 0B defense bill Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea MORE (R-Utah) — who want to use the looming fights over the debt ceiling and funding government operations to try to force President Obama to defund his signature program — and many establishment Republicans who see the effort as counterproductive and fanciful.

But conservative groups aren't capitulating. The Senate Conservatives Fund is standing with the Heritage Society, led by SCF founder and former Sen. Jim DeMint (R-S.C.), in warning Republicans not to back down on the issue.

This post was updated at 1:59 p.m.