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Lee's comments are in reference to an effort to block a continuing resolution on funding the federal government beyond Sept. 30 if that resolution includes funding President Obama's healthcare law.

"We just don't want to fund ObamaCare," Lee said on Laura Ingraham's radio show. "And I don't think Harry ReidHarry Mason ReidMcConnell not yet ready to change rules for Trump nominees The Hill's Morning Report — Sponsored by CVS Health — Trump’s love-hate relationship with the Senate Trump to press GOP on changing Senate rules MORE has the political wherewithal right now, given the dwindling support for this legislation by the American people, to shut down the government for ObamaCare. He doesn't want to go down in flames defending this law in that way."

Earlier on Wednesday, Sen. Roy BluntRoy Dean BluntSenate harassment bill runs into opposition from House Senate approves new sexual harassment policy for Congress Senators introduce bill to overhaul sexual harassment policy MORE (R-Mo.) said he opposed only raising the debt ceiling if ObamaCare was not funded.

"I think holding the debt limit hostage to any specific thing is probably not the best negotiating place," Blunt said.

Lee has said he's rallied enough Republicans to block a continuing resolution if that resolution continues to fund ObamaCare. Sens. John CornynJohn CornynRepublican leader: ‘For all practical purposes’ there’s no difference between an FBI informant and a spy Schumer: Congress must stop reported ZTE deal 'in its tracks' Hillicon Valley: Experts worry North Korea will retaliate with hacks over summit | FBI works to disrupt Russian botnet | Trump officials look to quell anger over ZTE | Obama makes case for tighter regs on tech MORE (Texas) and John ThuneJohn Randolph ThunePoll: 8 in 10 people in key states concerned about driverless cars Hillicon Valley: Mnuchin urges antitrust review of tech | Progressives want to break up Facebook | Classified election security briefing set for Tuesday | Tech CEOs face pressure to appear before Congress Senate GOP urges Trump administration to work closely with Congress on NAFTA MORE (S.D.), both members of the Republican Senate leadership, support Lee's effort, as do prominent Republicans like Sens. Marco RubioMarco Antonio RubioTrump appears to confirm deal on Chinese firm ZTE Hillicon Valley: Experts worry North Korea will retaliate with hacks over summit | FBI works to disrupt Russian botnet | Trump officials look to quell anger over ZTE | Obama makes case for tighter regs on tech Putting pressure on Trump, House passes bill barring government from doing business with ZTE MORE (Fla.) and Ted CruzRafael (Ted) Edward CruzGOP senators introduce Trump's plan to claw back billion in spending Pro-Trump super PAC raises .5 million in 6 weeks Trump has exposed Democratic hypocrisy on prison reform MORE (Texas).

Meanwhile, 64 House Republicans are pushing for a similar effort in their chamber.