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The National Council of La Raza sent an e-mail asking supporters to petition their senators to join the effort, while the New York Immigration Coalition held a news conference outside Mr. Schumer’s Manhattan office last week to demand that he introduce a bill before May 1.

Still, leaders say it’s more with sorrow than eagerness that they find themselves taking on the president, and several of them note that they voted for Mr. Obama and were among his vocal supporters in 2008.

“We were very patient because we said, understanding what else has to happen, we are going to do our job, and when you’re ready, our expectation is you’re going to move on this quickly,” Ms. Salas said. “Everything has been checked off the box, but every time we go back [and ask], is it time now, their explanation is, ‘Well, there’s something else.’ ”