(WASHINGTON) — The House of Representatives voted Thursday to block President Obama’s executive action on immigration, but in a different room of the Capitol, Republicans may have been offering a glimmer of hope.

The powerful Republican chairman of the House Rules Committee, Pete Sessions of Texas, said on the record that only the extreme members of his party want to deport non-criminal undocumented workers.

“There is no one in responsible Republican leadership, elected officials, who has said we should deport 13 or 11 million people,” Sessions said Thursday at a hearing on the president’s executive actions on immigration. “That is not what this effort is about.”

Sessions went on to promise that he and Virginia Republican Bob Goodlatte, the chairman of the House Judiciary Committee, would work on a bill in the new year.

"To have a well-understood agreement about what the law should be and how we should as communities, and farm communities, and tech communities create circumstances where we can have people be in this country and work,” he said. "And where not one person is quote ‘thrown out or deported.’ Where we do keep families together, but we do so under a rule of law of understanding."

The Texas congressman vigorously opposes the action taken by Obama, asserting that it oversteps presidential power. But he invited Democratic Congressman Luis Gutierrez of Illinois to help develop an immigration reform bill to replace it. Speaking directly to Gutierrez, who attended the Rules Committee hearing as a witness, Sessions vowed to work together.

“I’d ask that you to come back to the table… and work on this and I think you will find reasonableness will abound,” he said.

But Gutierrez remains skeptical about Republican action.

"Every time we have another vote to deport all 11 million immigrants and their families someone on the Republican side says, 'Oh, Luis. Just wait. The day when Republicans seriously address immigration, visas, border security and legal status is coming someday soon.’ But it never seems to come,” Gutierrez told ABC News. “It is always a higher priority to send a symbolic but meaningless message to the base that they are ‘getting tough’ rather than a serious message to the American people that they are getting serious about the immigration issue.”

Thursday, the House voted 219-197 to narrowly approve the Executive Amnesty Prevention Act, a bill that aims to prevent the president from implementing his executive actions. Although the bill is dead on arrival in the Democratic-controlled Senate, it may provide enough political cover to Republicans to prevent a government shutdown next week.

“The structure and stability of our democratic system depends upon the president executing the laws passed by Congress—not unilaterally rewriting them,” House Majority Leader Kevin McCarthy, R-California, wrote in a statement after the vote. “Today, the House made it very clear what the president is constitutionally and legally obligated to do.”

The president said during his announcement on executive action for immigration that should Congress pass a bill, it would trump his executive authority and he’d sign it into law.

“To those members of Congress who question my authority to make our immigration system work better, or question the wisdom of me acting where Congress has failed, I have one answer: Pass a bill,” he said.

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