The Senate Conservatives Fund (SCF) is targeting Sens. Lindsey GrahamLindsey GrahamOversight panel demands answers on Pentagon waste report Overnight Cybersecurity: Retired general picked to head DHS | Graham vows to probe Russian election interference Overnight Tech: AT&T, Time Warner CEOs defend merger before Congress | More tech execs join Trump team | Republican details path to undoing net neutrality MORE (R-S.C.) and Richard BurrRichard BurrTop Intel Dem: Congress 'far from consensus' on encryption Trump must be an advocate for the Small Business Administration Dems pledge to fight Sessions nomination 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 LeeMike LeeSenate sends annual defense bill to Obama's desk Overnight Healthcare: Medical cures bill finally heads to White House Overnight Energy: Trump taps EPA foe to head agency | Energy reform bill officially dead 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.