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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 McConnellAddison (Mitch) Mitchell McConnellFive things to know about efforts to repeal Obama's water rule Mulvaney aims to cement CFPB legacy by ensuring successor's confirmation Senate left in limbo by Trump tweets, House delays 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 LeeMichael (Mike) Shumway LeeFive things to know about efforts to repeal Obama's water rule Overnight Energy: EPA declines to write new rule for toxic spills | Senate blocks move to stop Obama water rule | EPA bought 'tactical' pants and polos Senate blocks bid to stop Obama water rule MORE (R-Utah), are circulating a letter pledging to oppose any budget that includes funding for ObamaCare.

Florida Sen. Marco RubioMarco Antonio RubioNew fears over Chinese espionage grip Washington Rubio heckled by protestors outside immigration detention facility Bill to protect work licenses of student loan debtors is welcome development MORE, Texas Sen. Ted CruzRafael (Ted) Edward CruzIt is time for Trump to start selling space exploration Senate left in limbo by Trump tweets, House delays The Hill's Morning Report — Sponsored by PhRMA — Immigration drama grips Washington MORE and Kentucky Sen. Rand PaulRandal (Rand) Howard PaulGOP senators call for probe of federal grants on climate change Overnight Health Care — Presented by the Association of American Medical Colleges — Key ObamaCare groups in limbo | Opioids sending thousands of kids into foster care | House passes bill allowing Medicaid to pay for opioid treatments US watchdog: 'We failed' to stem Afghan opium production 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."