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Mr. Rivera was the first to write legislation, and Sen. Marco Rubio, another Florida Republican who is viewed as a rising star in his party, has said he will do the same.

Mr. Rubio’s office didn’t respond to a request for comment Wednesday.

Rep. Luis V. Gutierrez, an Illinois Democrat who has taken a leadership role in pushing for broad immigration legislation, said he hasn’t studied the details of Mr. Rivera’s bill, but that he welcomes the debate.

“It is so rare lately that Republicans are interested in seriously discussing the immigration issue, so I want to be encouraging and keep an open mind,” Mr. Gutierrez said. “I am open to talking to anyone who has practical ideas about how to end the deportations that are splitting up families and destroying the dreams and futures of our young people.”

Republicans’ presumptive presidential nominee, Mitt Romney, has said he would veto the Dream Act, though he said he does support a path to citizenship for the narrow category of illegal immigrants who join the U.S. military.

President Obama is a strong supporter of the Dream Act.