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“He said, ‘Nuts!’” Mrs. Bachmann shouted outside the Capitol. “Today we look at this building and today we say to Republicans, to Democrats, to striped zebras, I don’t care who these people are, we say to them ‘Nuts’ because we are looking to the future.”

But other Republicans have warned that the defunding proposal would not survive the Democrat-led Senate and that Mr. Obama would veto any spending proposal that guts his signature domestic achievement. The resultant stalemate — and possible government shutdown — would damage the Republican image, they warn.

House Appropriations Committee Chairman Harold Rogers, Kentucky Republican, rolled out a proposal last week to fund the government through Dec. 15, effectively decoupling the fight over spending from the desire to gut Obamacare.

Conservatives, though, rebelled and rejected the plan, forcing Mr. Boehner to hold off on a vote.

Rep. Tim Huelskamp, Kansas Republican, told The Washington Times on Thursday that House leaders may have fallen out of touch with the GOP base, which is calling on them to follow through on their previous promises to do everything they can to scrap the law.

“If you want to pass something through the House, it has to defund Obamacare,” Mr. Huelskamp said.