"We just don't want to fund ObamaCare," Lee said on Laura Ingraham's radio show. "And I don't think Harry Reid 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 Blunt (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 Cornyn (Texas) and John Thune (S.D.), both members of the Republican Senate leadership, support Lee's effort, as do prominent Republicans like Sens. Marco Rubio (Fla.) and Ted Cruz (Texas).
Meanwhile, 64 House Republicans are pushing for a similar effort in their chamber.