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Others weren’t so sure.

Sen. Jeff Sessions, Alabama Republican and a member of the Senate Judiciary Committee, warned Wednesday against rushing an immigration bill through the Senate. He said Judiciary Chairman Patrick J. Leahy, Vermont Democrat, is outlining a timetable for the legislation that’s too rapid.

“Specifically, it seems the chairman is arguing we can put a bill on the floor two weeks after the Gang of Eight potentially produces legislation in early April,” Mr. Sessions said. “The massive proposal being cobbled together by a group of senators in secret must be independently judged and reviewed by the Judiciary Committee in the full light of day. That will take months — not two weeks.”

He added, “No member of Congress who believes in democratic procedure can acquiesce to the ramming through of a thousand-page bill that will dramatically and directly impact the taxes, wages and security of our constituents.”

President Obama, meanwhile, continued to apply pressure on lawmakers, saying in interviews with Univision and Telemundo, the nation’s two largest Spanish-language networks, that he is “optimistic” that when the senators get back to Capitol Hill, they will have a proposal that “meets the basic principles that I think are required for a strong bill.

“They are paying attention to border security, they are creating a way for people to earn their citizenship, they are improving the legal immigration system, and making sure that we can recruit the best and the brightest from all around the world that come here, invest here, and work here,” he told Univision.

The National Hispanic Leadership Agenda — a coalition of 30 religious, business and civic organizations — also looked to crank up the heat on lawmakers, launching a Hispanics United for Immigration Reform campaign in support of a comprehensive package that includes a pathway to citizenship.

“We are counting votes,” said Jose Calderon, president of the Hispanic Federation. “That is part of the work that the coalition does to make sure we can get over the top in terms of passing immigration reform this year, and so we are going to be targeting key congressional districts, key congressional members across America that are either on the fence or who we think we can get them over to our side.”

The group said Congress should revamp the visa system, should expedite family-based immigrant visas and must open the door for citizenship.

“If we are to restore the rule of law, the single most essential element of immigration reform is an earned legalization program with the real achievable road map to citizenship,” said Janet Murguia, president of the National Council of La Raza, the largest umbrella organization for Hispanic groups. “Not because enforcement is not important, but because enforcement is all we have done, and restoring the rule of law requires that we do both.”

• Dave Boyer contributed to this report.