And House Speaker John Boehner last week reassured his caucus he would stick to the rule on immigration reform and not schedule a vote without support of a majority of his caucus.
"I don't see any way of bringing an immigration bill to the floor that doesn't have a majority support of Republicans," Boehner told reporters last week after a non-public House GOP conference meeting.
Earlier in June, however, Boehner indicated on ABC's "Good Morning America," he might bring immigration reform to the floor even if it lacked the support of a majority of Republicans.
"What I'm committed to is a fair and open process on the floor of the House, so that all members have an opportunity," Boehner said. "It's not about what I want. It's about what the House wants. And my job is, as speaker, is to ensure that all members on both sides have a fair shot at their ideas."
Conservatives have been vocal in their desire to have Boehner on record as adhering to the unwritten rule named for former Speaker Dennis Hastert, R-Ill., that requires support of the "majority of the majority" before any bill is brought to the floor for consideration by the full House.
One GOP member who attended the meeting told The Hill Boehner had argued against the Hastert rule but assured his caucus he'd honor it on immigration, further complicating an already complicated issue.
In the Senate, immigration reform advocates have expressed optimism that the Democratic-led chamber's bipartisan bill will pass by the July 4 recess and think a strong majority -- read: more than 60 votes -- could provide the juice the measure needs to pass the Republican-controlled House.
But many GOP House (and Senate) members object to provisions that would provide a pathway to citizenship for the millions of illegal immigrants already in the country and want tougher border security provisions.
Enter discussions about the Hastert rule, which basically says no bill should pass the House on the backs of the minority party, or Democrats.
Rep. Dana Rohrabacher, R-Calif., has suggested Boehner be removed as speaker if he brings an immigration bill to the floor that doesn't carry the support of a majority of Republicans.
"I would consider that a betrayal of the Republican members of the House and a betrayal of Republicans throughout the country," Rohrabacher told WorldNetDaily in an interview published online. "If Speaker Boehner moves forward and permits this to come to a vote even though a majority of Republicans in the House oppose whatever is coming to a vote, he should be removed as speaker."
Boehner caught flak for allowing passage of the fiscal cliff vote on New Year's Day, when less than 40 percent of House Republicans supported the legislation, and the relief bill for states devastated in October by Hurricane Sandy, which passed in mid-January with fewer than 50 Republican votes. Several months later, the Violence Against Women Act reauthorization also passed sans support by a majority of Republicans.
The rule's namesake jumped on Boehner soon after the fiscal cliff and Hurricane Sandy legislation passed, warning Boehner that if he persists relying on Democratic votes to pass legislation, "you're not in power anymore."
"Maybe you can do it once, maybe you can do it twice, but when you start cutting deals where you have to get Democrats to pass the legislation, you're not in power anymore," Hastert said on Fox News Radio a couple of days after the fiscal cliff measure passed.
"When you start passing stuff that your members aren't in line with, all of a sudden your ability to lead is in jeopardy," Hastert said. "Because somebody else is making decisions. The president is making decisions, [House Minority Leader Nancy Pelosi] is making decisions, or they are making the decisions in the Senate. All tax bills and all spending bills, under the Constitution, start in the House. When you give up that responsibility you really give up your ability to govern, and that is the problem."
(Hastert, who was speaker from 1999 to 2007, broke his own rule in 2002 to pass the campaign finance reform bill, a bipartisan Senate measure co-sponsored by Sens. John McCain, R-Ariz., and Russ Feingold, a Democrat representing Wisconsin during his tenure.)
Freshman Rep. Matt Salmon, R-Ariz., a conservative, began circulating more than a month ago a petition on the matter, hoping to collect the required 50 signatures to force a vote in a special Republican Conference meeting on the matter. As recently as a couple of weeks ago, petition supporters haven't said how many signatures they've picked up, The Washington Post reported.
Boehner has publicly dismissed the effort and GOP aides privately told the Post they don't think a majority of House Republicans want to further hem in a leadership team already having fits corralling its caucus.
Republican aides said Salmon's provision would set up a system that would allow an internal vote before moving any legislation to the floor if at least 25 Republicans signed a letter requesting the internal gate-keeping tally. Legislation failing to pick up majority support in the internal vote won't be allowed to reach the floor.
"Codifying the Hastert Rule reinforces our resolve to consider legislation that doesn't grow government and doesn't cede legislative power to the minority party," Salmon said in a statement. "I believe this will actually strengthen the hands of our Republican leadership by fostering a unified voice among our conference."
His effort comes after leaders of conservative outside groups, including the heads of the Club for Growth and Heritage Action, sent a letter to Republican members asking them to codify the informal rule, Roll Call said.
"We are writing you today to encourage you to boldly use your majority not only to present a positive conservative vision, but also as the last backstop against the worst excesses of liberalism and Washington deal-making," they wrote. "Liberal Democrats control the White House and the Senate. We should not help their cause by handing them the keys to the House as well."
Hours after Boehner announced his intention not to bring the bill to the floor if it lacked support from a majority of Republicans, Sen. Robert Menendez, D-N.J., questioned the House speaker's commitment to immigration overhaul, Roll Call said.
"It is amazing and alarming that Speaker Boehner would allow a minority of House members -- who will never, ever support immigration reform -- to dictate the fate of bipartisan, comprehensive reform that an overwhelming majority of the American people want," said Menendez, a member of the bipartisan Senate "Gang of Eight," which negotiated the bipartisan overhaul. "You have to question the Republican leader's seriousness about real immigration reform if he is willing to put Tea Party politics ahead of the will of the American people. That's not in our national interest and it's certainly not about fixing our broken immigration system."
In his comments to reporters, Boehner took a shot at Democrats and the White House:
"I am increasingly concerned that the White House and Senate Democrats are -- would rather have this as an issue in the 2014 election, rather than to resolve it. It was the president who said that he wanted a robust vote coming out of the Senate, to help move this process along. And yet here's the president, and the Senate Democrats working to limit the number of Republican votes that this immigration bill is likely to get. I think that's unfortunate."
He later said: "I just think the White House and Senate Democrats are going to get very serious. We know that border security is absolutely essential. ... And I frankly think the Senate bill is weak on border security, I think the internal enforcement mechanisms are weak, and the triggers are almost laughable."
"And so if they're serious about getting an immigration bill finished, I think the president and Senate Democrats ought to reach out to their ... Republican colleagues, to build broad bipartisan support for the bill."