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.