Sen. Marco RubioMarco RubioScarborough: Trump has chosen the 'wrong side' THE MEMO: Trump reignites race firestorm RNC spokeswoman: GOP stands behind Trump's message 'of love and inclusiveness' 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 LeeTrouble draining the swamp? Try returning power to the states Congress must act to protect data privacy before courts make surveillance even easier Five tough decisions for the GOP on healthcare 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 CornynImmigration battlefield widens for Trump, GOP Congressional investigations — not just special counsels — strengthen our democracy Wrath of right falls on Google MORE (Texas) and John ThuneJohn ThuneWaymo taps Senate Commerce staffer for government affairs team Billboard ads target Republicans who want to roll back net neutrality GOP debates tax cuts vs. tax reform 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 media couldn't be more blatant in distorting Trump's words on Charlottesville Curtis wins GOP primary for House seat vacated by Jason Chaffetz Kimmel: Let’s make Trump a king so he has no power MORE (Texas).

A number of conservative groups are pressing Senate Majority Leader Mitch McConnellMitch McConnellTrump’s isolation grows Ellison: Trump has 'level of sympathy' for neo-Nazis, white supremacists Trump touts endorsement of second-place finisher in Alabama primary 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 Dean BluntGOP debates tax cuts vs. tax reform Five tough decisions for the GOP on healthcare Lacking White House plan, Senate focuses on infrastructure MORE (R-Mo.) and John McCainJohn McCainBush biographer: Trump has moved the goalpost for civilized society White House to pressure McConnell on ObamaCare McCain: Trump needs to state difference between bigots and those fighting hate 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.