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Some immigrant-rights groups have panned the Democratic bill as an unrealistic wish-list that has little chance of passage, and they have called on President Obama to get directly involved with House Republicans in trying to negotiate a final deal.

For his part, Mr. Denham bristled at the suggestion by Mr. Obama, repeated by Univision host Jorge Ramos, that House Republicans are the chief roadblock to legalizing illegal immigrants through a broad bill.

“That’s just not true,” Mr. Denham said. “You know, we need the president to show real leadership on this issue, as well as other issues that have really held up our schedule.”