ALBANY — With immigration still a contentious issue around the country, Gov. Andrew M. Cuomo and Republican lawmakers have maintained a noticeable distance from New York State proposals that would make financial aid available to illegal immigrants at colleges and universities.

Advocates for the so-called Dream Act have the backing of Mayor Michael R. Bloomberg, who said at a recent budget hearing that maintaining a system in which illegal immigrants cannot gain access to scholarship aid “is just asking us to continually have a group of people who can’t share in the American dream.”

But thus far the advocates have been unable to win public support from Mr. Cuomo, a Democrat who has generally been supportive of immigrants but who faces the possibility that his position could reverberate if he runs for president in 2016.

Mr. Cuomo’s spokesman would say only that the governor was studying the legislation.

Advocates for the legislation are also hoping to win support from at least some Republican lawmakers, as party leaders have increasingly promoted their outreach to the state’s fast-growing Hispanic population. But Republicans have so far issued only cautionary statements about the Dream Act.

New York, a state in which about 22 percent of the population is foreign-born, is one of a handful of states that allow illegal immigrants to receive in-state tuition at public universities. The City University of New York system has nearly 6,000 illegal immigrants enrolled at its schools, a spokesman said; the State University of New York does not track the immigration status of its students, according to its spokesman.

This year, seeking to broaden educational opportunities for residents who were brought to the United States illegally as children, lawmakers are offering several proposals to make it easier for them to pay for higher education.

Two versions of the Dream Act have been proposed in the State Legislature. One would allow illegal immigrants who graduated from a high school in the state to get a piece of the roughly $900 million in the state’s Tuition Assistance Program. The other bill would create a private fund that the students could tap for aid; donors would get tax credits for contributing to the fund.

These Dream Act proposals differ from federal legislation of the same name, backed by President Obama, which would create a path to citizenship for illegal immigrants who go to college or serve in the military. The federal bill was defeated in December 2010 and reintroduced last spring.

Daniela Alulema, a proponent of the New York version of the Dream Act and a board member at the New York State Youth Leadership Council, said the legislation would be an investment “in the education of undocumented youth.”

“These are young, dedicated, hard-working students who could be part of a more educated and productive work force,” Ms. Alulema said.

But critics are outraged.

The Dream Act “sends the message that there’s no distinction between being here legally or illegally,” said Steve Levy, the former Suffolk County executive and a vocal critic of the state’s immigration policies. “It’s hard enough that the government doesn’t enforce its borders, but now taxpayers would be subsidizing the undocumented residents.”

State Senator Adriano Espaillat, a Democrat from Washington Heights who is a sponsor of a version of the Dream Act, said he was hoping for “the political muscle of the governor” to get the measure passed.

“I haven’t heard him individually, voluntarily speak up on it,” Mr. Espaillat added. “That’s a concern, yes.”

Some advocates are optimistic that Mr. Cuomo will ultimately support the tuition measures, especially given his past support for immigrants.

“My instinct is, when the moment does come and he needs to come out, he will,” said Javier H. Valdés, the deputy director of Make the Road New York, an organization that has supported the bill.

Advocates for the legislation also argue that Republicans should back the measure, as the population of immigrants in some Republican districts rises. Several conservative pockets of the state, mostly on Long Island and in Westchester County, have growing Latino and immigrant populations.

“This is not a constituency that is just in Washington Heights or a constituency that is just in traditional communities of color,” said Bill Perkins, a Democratic senator from Harlem who is sponsoring a version of the Dream Act. “I think it offers those who might be Republicans the opportunity to bring something home to their base of support.”

Democrats are looking for support particularly from two freshman Republican senators from Long Island, Lee M. Zeldin and Jack M. Martins.

Mr. Zeldin, whose district is more than a quarter Hispanic, said he was keeping an open mind about the proposal but had questions about whether it would help some students at the expense of others. He said the government could also help immigrants by addressing areas like education, gang violence, foreclosures and property taxes.

“The fact is there are several issues we also are paying attention to,” Mr. Zeldin said. “I don’t see any one issue being an end all, be all to fix that community’s problems.”

Mr. Martins, whose district is 13.8 percent Hispanic, said he wanted to make sure the Dream Act was targeted at immigrants who arrived as children.

“The issue is far more prevalent and far more important,” he said, “when you’re dealing with younger children who’ve come to this country and are here for 10, 15 years and are literally as American as anyone else.”

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