In signal to McConnell, conservative group ties endorsement to support for defunding ObamaCare

The group is making a pledge to support a full repeal of the healthcare reform law, as well as opposing any bill or budget that includes funding or enforces any aspect of the law, a consideration in its endorsement process.

It's yet another indication that the group is keeping an eye on Senate Minority Leader Mitch McConnellMitch McConnellCures bill in jeopardy amid drug pricing push Senate Democratic super PAC sets fundraising record Five takeaways from Florida Senate debate 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 LeeDonald Trump's Mormon PR problem Trump's big worry isn't rigged elections, it's GOP establishment GOP senators avoid Trump questions on rigged election MORE (R-Utah), are circulating a letter pledging to oppose any budget that includes funding for ObamaCare.

Florida Sen. Marco RubioMarco RubioFive takeaways from New Hampshire Senate debate Obama plans 'aggressive' blitz for Clinton in campaign's final days One way or another, 2016 was all about Donald Trump's hands MORE, Texas Sen. Ted CruzTed CruzDemocrats pounce on Cruz's Supreme Court comments Brent Budowsky: An epic battle for the future of Congress Cruz: Precedent exists for keeping Supreme Court short-staffed MORE and Kentucky Sen. Rand PaulRand PaulWhat the 'Bernie Sanders wing of the GOP' can teach Congress GOP senators avoid Trump questions on rigged election How low is the bar for presidential candidates, anyway? 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."