Ground zero in the establishment-strikes-back fight may be the House race in Idaho between Representative Mike Simpson, an eight-term member, and Bryan Smith, a lawyer who has the backing of the anti-tax, anti-spending group the Club for Growth. The U.S. Chamber of Commerce has started running ads depicting Mr. Simpson as the true conservative, rebutting Mr. Smith’s claim that he is a “RINO” — Republican in name only.

Mr. Smith said he had anticipated the pushback, but was seeing encouraging support locally. “I always knew that a 15-year incumbent who’s a close ally of John Boehner’s was going to outraise me,” he said before ticking off some recent triumphs. “We’ve raised over half a million dollars. Last week I got two more endorsements from the Republican Party on the county level.”

Mr. Reed, of the chamber, said he had it on good authority that his message to the more recalcitrant Republicans was sinking in.

“Boehner has told me that in the House caucus meetings there are a lot more guys sitting up straight,” he said. “They aren’t sitting in the back with their feet up on the chairs hurling spitballs.”