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Jorge Ramos, an anchor at Univision, a Spanish-language network, visited the Capitol on Thursday to press Mr. Boehner and Mr. Reid for action.

“You can do it, Mr. Speaker. You can do it, and you really haven’t done it,” Mr. Ramos told Mr. Boehner.

Mr. Boehner said there is “nobody more interested in fixing this problem than I am,” but he pointed to Republicans’ distrust of Mr. Obama as the chief roadblock.

At Mr. Reid’s press conference minutes later, Mr. Ramos demanded to know why the Democratic leader was “keeping hope alive.”

“Isn’t it time just to say, ‘Nothing’s going to happen, no immigration reform’?” Mr. Ramos said.

Mr. Reid replied that Democrats have given House Republicans a final window.

“We waited 329 days; we’re willing to wait another six weeks,” he said. “But at the end of six weeks, if something hasn’t been done, then there’s going to have to be a move made.”