It's yet another indication that the group is keeping an eye on Senate Minority Leader Mitch McConnell'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 Lee (R-Utah), are circulating a letter pledging to oppose any budget that includes funding for ObamaCare.
Florida Sen. Marco Rubio, Texas Sen. Ted Cruz and Kentucky Sen. Rand Paul 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."