It's yet another indication that the group is keeping an eye on Senate Minority Leader Mitch McConnellMitch McConnellClinton, Trump sharpen attacks Sanders, Merkley back McConnell decision to skip TPP vote John McCain: No longer a profile in courage MORE's (R-Ky.) primary fight. The group said recently it was open to backing primary challenger Matt Bevin, and McConnell has so far refused to support efforts to defund ObamaCare.
Bevin picked up the endorsement of another conservative group, the Madison Project, on Monday.
"A lot of Republicans say they oppose Obamacare when they're campaigning, but few are actually willing to do what it takes to stop it," said Senate Conservatives Fund Executive Director Matt Hoskins in a release. "This new pledge is for those who are willing to fight Obamacare by supporting its repeal and also by opposing its funding."
The pledge comes as a handful of conservative Senators, led by Sen. Mike LeeMike LeeThe impact of silence: The incarceration of children who have committed no crime Fidelity denies lobbying for student loan tax break Cruz, Lee question legality of Iran payment MORE (R-Utah), are circulating a letter pledging to oppose any budget that includes funding for ObamaCare.
Florida Sen. Marco RubioMarco RubioLatino Republicans split on Trump's outreach Illegal immigration foe: Trump shift the 'death knell of his candidacy' Analysis: Clinton speaks at higher grade level than Trump MORE, Texas Sen. Ted CruzTed CruzThe Trail 2016: On the fringe FULL SPEECH: Hillary Clinton links Trump to 'alt-right' in Reno Presidential hopefuls still bank on retail politics MORE and Kentucky Sen. Rand PaulRand PaulTrump, Clinton boost Snapchat spending Clinton enjoying edge over Trump in Silicon Valley Trump gets little backing from Silicon Valley MORE have all signed the letter, but other Republicans have criticized it, calling what amounts to a threat to shut down the government over ObamaCare unreasonable and unrealistic.
Lee insisted on Sunday his effort is not an attempt to shut down the government.
"We all know the government is going to get funded. The only question is if the government gets funded with ObamaCare or without it," said Lee on “Fox News Sunday.” "If we can delay it, we can stop its consequences, at least for now."