House Speaker John A. Boehner (R-Ohio) privately reiterated to colleagues Tuesday that the House will not vote on an immigration reform package that doesn’t have the support of a majority of Republicans.

House Speaker John A. Boehner (R-Ohio). (Alex Brandon/AP)

The comments came as some of the most conservative GOP lawmakers and well-financed outside conservative groups are seeking to change internal House GOP rules that would block legislation from the House floor that does not have “majority-of-the-majority” support.

Boehner (R-Ohio) acknowledged Tuesday that the so-called "Hastert Rule" -- named after the former House speaker -- was violated this year when the House voted to approve the "fiscal cliff" spending deal and federal funding for communities ravaged by Hurricane Sandy, according to senior GOP aides familiar with his comments.

On immigration, however, Boehner said that Republicans enjoy "plenty of leverage" on the issue and will not need to rely on Democratic votes to pass a bill.

"I have no intention of putting a bill on the floor that will violate the principles of our majority and divide our conference," Boehner said, according to the GOP aides. "One of our principles is border security. I have no intention of putting a bill on the floor that the people in this room do not believe secures our borders. It’s not gonna happen."

The assurances made behind closed doors Tuesday differ slightly from public comments Boehner made last week, when he told reporters that he didn't intend to hold a vote on an immigration bill "that violates what I and what my members of my party, what our principles are" and that he expected to continue earning "strong bipartisan majorities" for bills brought to the floor.

Boehner's apparent sharpened resolve comes at a critical moment in the months-long attempts to overhaul the nation's immigration laws, as the Senate is poised to begin voting on amendments to its comprehensive bipartisan proposal Tuesday and bipartisan talks in the House are at a stalemate over several lingering issues of concerns.

Meanwhile, the House Judiciary Committee began debating a immigration proposal Tuesday that is strongly opposed by congressional Democrats and immigrant rights advocates, some of whom opted to loudly disrupt the start of the proceedings.

As House Judiciary Committee Chairman Bob Goodlatte (R-Va.) began a hearing on the bill, several people sitting towards the front of the hearing room stood and began shouting, "Shame shame shame, stop the pain."

U.S. Capitol Police officers stepped in to remove the protesters, who continued chanting "Si se puede" -- or "Yes we can," in English -- in the hallways outside.

"This does not help their cause. This is unhelpful to orderly process and I urge everyone here to follow the recommendations of the chairman," the ranking Democrat on the committee, Rep. John Conyers (Mich.), said as the chanting could be heard continuing outside the room.

The Republican-backed proposal under consideration would give state and local law enforcement authorities more power to arrest and charge immigrants for overstaying visas or entering the U.S. illegally.

The SAFE Act (Strengthen and Fortify Enforcement Act) also would make it a federal misdemeanor to be "unlawfully present" in the U.S. and would permit state and local governments to draft their own immigration laws, as long as they are consistent with federal statutes. Finally, local law enforcement agencies would be eligible for new federal grants to enforce the immigration laws.

Goodlatte described the plan as "a game-changing piece of legislation" that will bolster attempts to track illegal immigrants far beyond the borders.

"We can’t just be fixated with securing the border. We must also focus on what to do with aliens who make it past the border," he said.

But Conyers described the proposal as "extreme and heinous," saying it would jeopardize public safety by making local police officers de facto immigration agents and "force them to make public safety a distant second priority." Worse, Conyers said, the changes would deter crime victims and eyewitnesses from reporting crimes or providing assistance to local police if they fear potential deportation.

The panel is scheduled to begin debating the immigration proposal Tuesday with a final vote expected on Wednesday, according to aides.

Rep. Trey Gowdy (R-S.C.), the bill's chief sponsor, said his proposal is just one of several that will be considered by the committee as it pursues "a remedy" to the nation's broken immigration system "step-by-step and increment-by-increment."

"This is just the first step. It is a first step in what everyone agrees to be a longer journey," Gowdy added.

Rep. Luis Guitierrez (D-Ill.), who is one of four Democrats seeking to negotiate a bipartisan immigration bill in the House, blasted the Gowdy bill Tuesday morning, saying it runs the risk of sapping any goodwill Republicans may have established on the issue since admitting in the weeks after last year's elections that the party needed to work on overhauling immigration laws.

"On the other side of the aisle, it is hard to talk about immigrants in a new way when your party, its platform, its candidates, its talk-radio and TV personalities have spoken disparagingly about immigrants for years," he said in remarks on the House floor.  "When you reference gang-bangers, drunk-drivers, and rapists every time you talk about immigrants, it is hard to switch gears quickly."

"Do not push forward a bill that criminalizes every immigrant family and makes everyone think twice before they call 9-1-1," Gutierrez told his GOP colleagues. "You are better than this."

This story has been updated.

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