Sen. Marco RubioMarco RubioTop Trump officials push border wall as government shutdown looms Rubio defends Trump: 'This whole flip-flop thing is a political thing' Rubio: Shutdown would have 'catastrophic impact' on global affairs 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 LeeTrump should work with Congress to block regulations on prepaid cards Sweeping change at DOJ under Sessions Executive orders alone can't create sustainable deregulatory change 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 CornynJuan Williams: Trump's 100 days wound GOP Trump wall faces skepticism on border No Congress members along Mexico border support funding Trump's wall MORE (Texas) and John ThuneJohn ThuneSeven major players in Trump's trillion infrastructure push Trump’s great tech opportunity is in spectrum sharing Norquist warns GOP: Don’t link taxes, infrastructure 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 CruzWeek ahead in tech: Trump's antitrust pick heads before Senate Week ahead: Senate panel to vote on Trump's FDA pick Warren builds her brand with 2020 down the road MORE (Texas).

A number of conservative groups are pressing Senate Majority Leader Mitch McConnellMitch McConnellOvernight Finance: Trump wants 15 percent corporate rate | GOP tax team huddles with Trump aides | Shutdown watch over border wall McConnell: No deal yet on government funding Trump team to meet with congressional leaders on tax reform 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 BluntThis week: Congress returns to government shutdown fight AACR’s march on Washington Five hurdles to avoiding a government shutdown MORE (R-Mo.) and John McCainJohn McCainBeyond Manafort: Both parties deal with pro-Russian Ukrainians With help from US, transformative change in Iran is within reach The Hill's 12:30 Report 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.