Sen. Marco RubioMarco RubioWill Republicans stand up to the NRA's insurrection rhetoric? The Hill's Whip List: Senate ObamaCare repeal bill Ivanka Trump turns to House GOP on paid family leave MORE (R-Fla.) argued Thursday that it’s President Obama, not Republican leaders in the House and Senate, who is responsible for threats of a government shutdown over the implementation of ObamaCare.

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"This September, Congress will have to pass another short term spending bill to fund the federal government,” Rubio wrote in an op-ed for Fox News. 

“We should pass one that keeps the government open, but doesn't waste any more money on ObamaCare. The president and his allies – and even some Republicans – will accuse us of threatening to shut down the government. In fact, it is President Obama who insists on shutting down the government unless it funds his failed ObamaCare experiment.”

Sen. Mike LeeMike LeeRocky rollout for Senate healthcare bill Overnight Healthcare: Latest on Senate healthcare bill | Four conservatives say they'll oppose | Obama slams bill | Health groups offer scathing criticism Four Senate conservatives say they oppose ObamaCare repeal bill MORE (R-Utah) says he’s recruited more than a dozen Republican colleagues willing to shut down the government by blocking a continuing resolution to fund the government beyond Sept. 30 if it includes funding for ObamaCare.

The second- and third-ranking members of Republican leadership, Sens. John CornynJohn CornynLawmakers want meeting with Trump administration to take US-Mexico border trade Rocky rollout for Senate healthcare bill The Hill's Whip List: Senate ObamaCare repeal bill MORE (Texas) and John ThuneJohn ThuneSenate panel unveils aviation bill with consumer protections, drone fix Four Senate conservatives say they oppose ObamaCare repeal bill Live coverage: Senate GOP unveils its ObamaCare repeal bill MORE (S.D.), have said they support Lee’s plan, as do influential conservatives and potential presidential candidates Sens. Marco Rubio (Fla.) and Ted CruzTed CruzWill Republicans stand up to the NRA's insurrection rhetoric? Rocky rollout for Senate healthcare bill Overnight Healthcare: Latest on Senate healthcare bill | Four conservatives say they'll oppose | Obama slams bill | Health groups offer scathing criticism MORE (Texas).

A number of conservative groups are pressing Senate Majority Leader Mitch McConnellMitch McConnellRocky rollout for Senate healthcare bill Overnight Healthcare: Latest on Senate healthcare bill | Four conservatives say they'll oppose | Obama slams bill | Health groups offer scathing criticism Sanders: I hope McConnell listened to protesters outside his office MORE (R-Ky.) to back Lee. Heritage Action endorsed the effort on Tuesday, and the Club for Growth penned a letter to McConnell on Wednesday urging him to sign on to the plan.

In addition, 64 House members have signed on to a similar effort to try and block the president’s signature healthcare reform law, with some arguing the GOP could use the debt ceiling as leverage against its implementation.

However, two Republican senators – Roy BluntRoy BluntOvernight Regulation: Senate Banking panel huddles with regulators on bank relief | FCC proposes 2M fine on robocaller | Yellowstone grizzly loses endangered protection Overnight Finance: Big US banks pass Fed stress tests | Senate bill repeals most ObamaCare taxes | Senate expected to pass Russian sanctions bill for second time GOP senator: 'No reason' to try to work with Dems on healthcare MORE (R-Mo.) and John McCainJohn McCainCoats: Trump seemed obsessed with Russia probe The Hill's Whip List: Senate ObamaCare repeal bill Meghan McCain slams 'felon' Dinesh D'Souza over tweets mocking father's captivity MORE (R-Ariz.) say they oppose efforts to shut down the government to block funding for ObamaCare.

Rubio on Thursday said the law should be replaced with “market-based” reforms.

“It is time to admit that ObamaCare isn't going to work, decide not to waste a single cent more on it, and replace it with market-based reforms that will give people more health insurance choices and options,” he wrote.