Sen. Marco RubioMarco RubioWhat Trump's Cabinet picks reveal House passes water bill with Flint aid, drought relief What the 2016 election can tell us about 2018 midterms 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 LeeSenate sends annual defense bill to Obama's desk Overnight Healthcare: Medical cures bill finally heads to White House Overnight Energy: Trump taps EPA foe to head agency | Energy reform bill officially dead 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 CornynSenate Democrats dig in as shutdown approaches Overnight Energy: Fight over miners' benefits risks shutdown | Flint aid crosses finish line in House Overnight Finance: Senate Dems dig in as shutdown looms | Trump taps fast-food exec for Labor chief | Portland's new CEO tax MORE (Texas) and John ThuneJohn ThuneOvernight Tech: Last-ditch effort to get Dem FCC commish confirmed | Facebook's Sandberg on fake news | Microsoft completes LinkedIn deal FCC chairman willing to resign to get colleague confirmed Overnight Tech: AT&T, Time Warner CEOs defend merger before Congress | More tech execs join Trump team | Republican details path to undoing net neutrality 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 CruzThe Hill's 12:30 Report Cruz defends Trump's Taiwan call Ark., Texas senators put cheese dip vs. queso to the test MORE (Texas).

A number of conservative groups are pressing Senate Majority Leader Mitch McConnellMitch McConnellSenate Democrats dig in as shutdown approaches Overnight Healthcare: Burwell huddles with Dems on fighting ObamaCare repeal Reid: Bring back the earmarks 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 BluntSanders: GOP blocked 'Trump proposal' to lower drug prices McConnell: We'll start Obamacare repeal on day one Could bipartisanship rise with Trump government? MORE (R-Mo.) and John McCainJohn McCainSenate votes to elevate Cyber Command in military Senate sends annual defense bill to Obama's desk Trump really can't do much to reduce tensions with Putin's Russia 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.