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Brooks dismissed that assessment.

“That’s bunk. Next question,” he told reporters.

Rep. Luis Gutierrez, D-Ill., an outspoken immigration overhaul supporter, said he was backing Denham’s effort even if it would amount to an incomplete victory. He also disputed the idea that the quick action by conservatives in the caucus to shut Denham down showed that no action on immigration is possible.

“I believe there’s still a great deal of support,” Gutierrez said. “I say let’s have a victory.”

Gutierrez contended that without action by the House, Obama will act on his own authority by summer to protect more groups of immigrants from deportation.

Last month, Obama asked Homeland Security Secretary Jeh Johnson to review enforcement practices to ease his administration’s rate of deportations. Under Obama’s leadership, almost 2 million people have been removed from the U.S.

The Congressional Hispanic Caucus has circulated a draft memorandum of possible recommendations to Johnson, including a proposal similar to Denham’s legislation and an expansion of the step Obama took in June 2012 allowing young people who immigrated illegally into the United States - so-called DREAMers - to remain in the country under certain conditions. They take their name from the Development, Relief and Education for Alien Minors, or DREAM, Act, which is stymied in Congress and would provide a way for them to permanently remain in the U.S.

The caucus said that expansion should apply to the parents of the young people.

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Associated Press writer Erica Werner contributed to this report.