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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 ReidDems search for winning playbook Dems face hard choice for State of the Union response The Memo: Immigration battle tests activists’ muscle 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 BluntGOP senators eager for Romney to join them Senate GOP wary of ending Russia probes, despite pressure GOP on precipice of major end-of-year tax victory 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 CornynMcCarthy: ‘No deadline on DACA’ NSA spying program overcomes key Senate hurdle Hoyer suggests Dems won't support spending bill without DACA fix MORE (Texas) and John ThuneJohn Randolph ThuneWeek ahead: Tech giants to testify on extremist content Overnight Tech: GOP senator presses Apple over phone slowdowns | YouTube cancels projects with Logan Paul after suicide video | CEOs push for DACA fix | Bill would punish credit agencies for breaches GOP senator presses Apple on phone slowdowns MORE (S.D.), both members of the Republican Senate leadership, support Lee's effort, as do prominent Republicans like Sens. Marco RubioMarco Antonio RubioOvernight Cybersecurity: Bipartisan bill aims to deter election interference | Russian hackers target Senate | House Intel panel subpoenas Bannon | DHS giving 'active defense' cyber tools to private sector Senators unveil bipartisan push to deter future election interference Puerto Rico's children need recovery funds MORE (Fla.) and Ted CruzRafael (Ted) Edward CruzWith religious liberty memo, Trump made America free to be faithful again Interstate compacts aren't the right way to fix occupational licensing laws Texas Dem: ‘I don’t know what to believe’ about what Trump wants for wall MORE (Texas).

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