Speaking at a Capitol Hill panel organized by the Heritage Foundation, Salmon said there's "great unrest" among Republicans about the violations of the majority-of-the-majority principle this year. GOP leaders have this year brought up four bills without the support of most House Republicans -- including legislation to avert the fiscal cliff, provide aid to Hurricane Sandy victims and reauthorize the Violence Against Women Act.
Rep. Tom McClintock (R-CA) issued the same threat.
"The American people elected a Republican majority to the House of Representatives," McClintock said. "Were a leader of that majority to use his authority to circumvent that majority, that would be cause for removal in my judgment."
Boehner's job security is perennially in question, but he faces unusually strong and competing pressures on the issue of immigration. As the country's most powerful Republican, he has to worry about his party's future, which is threatened if it blocks reform. As Speaker, he has to worry about members of his House majority, who could be threatened by primaries if they vote for a bill that isn't palatable to the hard right. The Senate is set to pass its immigration reform bill with a strong bipartisan supermajority on Thursday.
Rep. Raul Labrador (R-ID) said Republicans are "running around like chickens with our heads cut off thinking that we have to do [immigration reform] for political reasons." He said the farm bill fiasco last week was "very instructive" for Republicans, arguing that the legislation failed because GOP leaders relied on Democrats.
"So our leadership needs to take a lesson from this: Stop negotiating with Democrats," he said. "Start doing what is the right policy -- the right conservative policy for America."
Salmon said he's organizing an internal GOP petition to codify the Hastert Rule and that he's making good progress. "I do believe most members of our conference will believe that legislation that we pass should be majority legislation," he said.
So far Boehner is insisting he'll stick by the Hastert Rule on immigration. He has already rejected the Senate bill and said the House will go its own way on reform depending on how Republicans want to proceed. On Thursday he said he'll apply the same majority-of-the-majority principle to the final House-Senate legislation that emerges from conference committee.
Boehner received 220 votes in the January election for Speaker, barely clearing the 218-vote threshold necessary to secure victory. He told reporters Thursday that House Republicans will meet on July 10 to discuss the path forward on immigration reform.