Sen. Tom Coburn (R-Okla.) is very much opposed to efforts by some conservative lawmakers to defund the Affordable Care Act.

(J. Scott Applewhite/AP) Sen. Tom Coburn (J. Scott Applewhite/AP)

“I’d be leading the charge if I thought this would work. But it will not work," he told the Washington Examiner of the plan to block any budget bill that includes funding for the health-care law. Sens. Marco Rubio (R-Fla.) and Mike Lee (R-Utah) are behind the push.Coburn predicts that such a demand would only succeed in producing a government shutdown for which Republicans will be blamed. “The strategy that has been laid out is a good way for Republicans to lose the House," Coburn said. "I’m getting phone calls from Oklahoma saying, ‘Support Mike Lee,’ and I’m ramming right back: 'Support him in destroying the Republican party?'”

The conservative senator is well known for his opposition to any legislation he sees as wasteful spending; he's nicknamed "Dr. No."

Sen. Richard Burr (R-N.C.) has also been skeptical of the Obamacare defunding plan. Earlier this week he called the defunding push "the dumbest idea I've ever heard."

On Rubio and Lee's side are Sens. Jeffrey Chiesa (N.J.), Mike Enzi (Wyo.), Deb Fischer (Neb.), Chuck Grassley (Iowa), James Inhofe (Okla.), Rand Paul (Ky.), Jim Risch (Idaho), John Thune (S.D.), David Vitter (La.). The anti-tax Club for Growth is also supportive. Three other Senate Republicans have removed their names, reportedly under pressure from leadership. According to the Examiner, Republican aides predict that there would be enough votes to overcome a filibuster on the continuing resolution.

Senate Minority Leader Mitch McConnell (R-Ky.) plans to hold a vote on an amendment to defund Obamacare. But the leadership has not supported the threat to block any budget deal without it. House Speaker John Boehner (R-Ohio), who has more power to block a budget agreement in the Republican-majority House, has also been noncommittal.