WASHINGTON – Sen. Bob Menendez expressed displeasure Tuesday over House Speaker John Boehner’s decision to withhold consideration of any immigration reform measure that doesn’t have the support of the majority of the Republican caucus.

Menendez (D-N.J.), a member of the Gang of Eight, a bipartisan group of upper-chamber lawmakers who have pieced together a delicate immigration compromise, questioned Boehner’s seriousness about addressing the issue “if he is willing to put tea party politics ahead of the will of the American people.”

“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,” Menendez said.

The decision, Menendez said, is “not in our national interest and it’s certainly not about fixing our broken immigration system.”

Earlier Tuesday, Boehner (R-Ohio) told reporters that he could not envision a scenario where he would permit debate over immigration reform if most members of the Republican majority in the House didn’t offer their support.

Boehner said the only time he will consider bringing an issue to the floor without the support of his caucus is “when there is zero leverage.” That has occurred during his tenure in the chair on occasion – most recently when the lower chamber voted on Hurricane Sandy relief – but only when “we faced a worse alternative, politically or in terms of policy.”

That is not the case in this instant, Boehner said, so he is obliged to implement what is popularly known as the Hastert rule, named after former House Speaker Denny Hastert, an Illinois Republican who took great pains to satisfy his caucus.

“We have plenty of leverage,” Boehner said. “And I have no intention of putting a bill on the floor that will violate the principles of our majority and divide our conference. 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 going to happen.”

Boehner to this point has been coy about how he intended to address immigration reform, which is making its way through the Senate with a vote slated before July 4. But he has been under pressure from GOP lawmakers, particularly those with a conservative bent, to take a stand.

Rep. Dana Rohrabacher (R-Calif.), appearing on World Net Daily radio, said earlier this week that Boehner should be ousted if he doesn’t adhere to the Hastert rule.

“I would consider that a betrayal of the Republican members of the House and a betrayal of the Republicans throughout the country,” Rohrabacher said. “If Boehner moves forward and permits this to come to a vote even though the majority of Republicans in the House — and that’s if they do — oppose what’s coming to a vote, he should be removed as speaker.”

Senate Democratic Leader Harry Reid, of Nevada, said Tuesday that he told Menendez and other Democratic members of the Gang of Eight to concentrate on getting the measure through the Senate and not concern themselves with Boehner’s comments. Sooner or later, Reid said, the House will be forced to act.

“No matter what he has said, there’s going to be significant national pressure on the House to do something on immigration,” Reid said. “I’m only worried about what’s going to happen here and I’m not going to say how I really feel about it, OK?”

The House Judiciary Committee on Tuesday began a mark-up on what is called the SAFE Act, which provides local police the authority to arrest illegal immigrants and transfer them to federal custody and expands the number of detention facilities for those awaiting deportation. Other immigration bills are to follow.

Rep. Bob Goodlatte (R-Va.), chairman of the House Judiciary Committee, has expressed a desire to consider individual pieces of immigration legislation rather than follow the Senate’s lead and work on a single comprehensive reform measure.

The Senate, meanwhile, is continuing debate on the Border Security, Economic Opportunity and Immigration Modernization Act of 2013, which creates a pathway to citizenship for the estimated 11 million immigrants who entered or remained in the country without proper documentation.

Under the bill, illegal immigrants who have resided in the U.S. since Dec. 13, 2011, must seek provisional legal status that allows them to work but renders them ineligible for federal benefits. They must pay a penalty, taxes, and a processing fee and can only apply for permanent status after 10 years.

A new visa program for low-skilled workers would be developed and the Department of Homeland Security would be charged with coming up with a $4.5 billion plan to gain effective control of the porous Southern border with Mexico.