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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 McConnellOvernight Healthcare: High drama for ObamaCare vote | Freedom Caucus chair 'optimistic' about deal | Trump woos right High drama for ObamaCare vote Senate nixes Obama-era workplace safety rule 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 LeeRepublicans should seize the moment and repeal ObamaCare now ObamaCare repeal faces last obstacle before House vote Live coverage: Day three of Supreme Court nominee hearing MORE (R-Utah), are circulating a letter pledging to oppose any budget that includes funding for ObamaCare.

Florida Sen. Marco RubioMarco RubioDem senator: House Intel chairman may have revealed classified info Five takeaways from Labor pick’s confirmation hearing GOP insists FBI probe won’t slow up Trump MORE, Texas Sen. Ted CruzTed CruzBudowsky: Trump’s war against truth Five takeaways from Labor pick’s confirmation hearing Republicans should seize the moment and repeal ObamaCare now MORE and Kentucky Sen. Rand PaulRand PaulGOP rep: Trump could be 'one-term president' if healthcare bill passes Overnight Defense: Pentagon chief urges Congress to approve budget boost | Senate fight over NATO addition Defying Trump, Freedom Caucus insists it'll oppose GOP ObamaCare replacement 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."