House Majority Whip Kevin McCarthy (R-Calif.) on Sunday would not rule out passage of bills without the support of a majority of the chamber's Republicans, saying only that Speaker BoehnerJohn BoehnerEXCLUSIVE: Pro-Hillary group takes 0K in banned donations Ryan: Benghazi report shows administration's failures Clinton can't escape Benghazi responsibility MORE (R-Ohio) was committed to finding GOP support for major legislation.
House GOP leadership has recently violated the "Hastert rule," named after former Republican Speaker Dennis Hastert (Ill.), which requires bills coming to the floor to have support from the majority of GOP members.
“The speaker says he wants to, if you listen to his press conference the other day, he will pass bills that the House passes,” said McCarthy on CNN’s "State of the Union." “He'll pass bills that the Republicans are moving forward.”
The House in recent months broke the Hastert rule three times in passing bills to avoid the "fiscal cliff" by raising tax rates on some earners, Hurricane Sandy relief, and the Violence Against Women Act.
Boehner on Tuesday, though, said that he would not make a habit of passing bills lacking majority GOP support.
“It’s not a practice I would expect to continue long-term,” Boehner said.
McCarthy on Sunday cautioned against underestimating the ability of the House to move legislation on key issues forward.
"It is better if the House does their work. We should be sending bills to the Senate," McCarthy said.
Asked about immigration specifically, McCarthy touted the House's ability to move forward with its own plan, rather than waiting to take up a potential Senate-passed bill.
"I would not underestimate the House's ability to pass an immigration bill," he said. "I think we have plenty of ideas on that and I think that we can move the ball as well."
CNN host Candy Crowley said of her Hastert rule question: "I think I am not going to get a straight answer to that."
In a statement to The Hill, McCarthy spokesperson Mike Long said: "Whip McCarthy strongly supports returning to regular order to bring legislation to the floor that has the support of a majority of the majority. Insinuation to the contrary is completely false."
Boehner has never explicitly endorsed the Hastert rule, but has said he would only bring bills to the floor that were backed by a “majority of the majority.
The speaker has pledged to let the House “work its will,” but has faced criticism from conservative members over House passage of Democratic-backed legislation.
This story was updated at 8:01 p.m. to include a response from Rep. McCarthy's office.