AUSTIN, Texas » A new survey shows that Hispanics, the nation’s largest minority group, have grown increasingly negative toward the Republican Party during the political battle over changing immigration law and lean surprisingly liberal on social issues like gay marriage — a combination of factors that presents a steep challenge for Republicans in trying to win back Hispanic voters.

More than 6 in 10 Hispanic respondents said they felt closer to the Democratic Party than they had in the past, while only 3 in 10 said they felt closer to the Republican Party. When Hispanics were asked to offer descriptions of the parties, 48 percent of the responses about the Republicans were negative associations like "intolerant" and "out of touch," while 22 percent of the responses for the Democrats were negative.

The outlook for Republicans has grown increasingly negative since 2004, when President George W. Bush won re-election with 44 percent of the Hispanic vote. The survey, released Friday by the Public Religion Research Institute, a nonprofit research group in Washington, found that 56 percent of registered Hispanic voters identified with the Democrats, while 19 percent said they identified with Republicans, and 19 percent as independents.

The religious identities of Hispanics are also changing, with 69 percent saying they grew up Catholic, but only 53 percent saying they identify as Catholic now. Those saying they are evangelical Protestants have increased 6 percentage points to 13 percent. But Hispanics, like Americans as a whole, are increasingly claiming no religion at all: 7 percent of Hispanics say they were raised in a faith but now have no religious affiliation, bringing the total percentage of Hispanics with no religion to 12 percent.

Robert P. Jones, chief executive of the institute, said in an interview: "If these trends continue, what we’ll see is a growing polarization among Hispanics, anchored on one end by evangelicals, who tend to be conservative, and on the other end by religiously unaffiliated Hispanics. The unaffiliated voted for Obama by 80 percent, so you see really different political profiles."

Conservatives have often claimed that Hispanics are a natural constituency for the Republican Party because they care about what the party considers family values. This holds true on abortion, with 52 percent saying abortion should be illegal in all or most cases, and 47 percent saying it should be legal. But on gay marriage, 55 percent of Hispanics favor allowing gay and lesbian couples to marry, compared with 43 percent who are opposed.

And Hispanics in the poll said they were far more likely to vote for candidates based on their stances on immigration than on their stance on abortion or same-sex marriage.

The parties’ handling of immigration has been a major factor swaying Hispanics’ allegiances. In the survey, 42 percent of Hispanics said Democrats were better able to deal with immigration, while 16 percent said Republicans would do better.

But in a finding that could be tantalizing for both parties, 21 percent of Hispanics polled said neither party is best able to handle immigration, and 17 percent said both parties are equally able to deal with immigration. About one in five registered Hispanic voters and more than one-third of Hispanic citizens who are not registered to vote said they were independents, suggesting they might be up for grabs between the parties.

Latinos named health care as one of their primary concerns, and they were sharply divided on President Barack Obama’s health care law. Nearly half, 48 percent, said they would support repealing the law, while 47 percent opposed repeal, a finding that could be promising for Republicans battling that law.

Hispanics in the poll had strong ideas about resolving illegal immigration. Sixty-seven percent of Latinos surveyed said unauthorized immigrants in the country should be allowed to become American citizens if they meet certain requirements. Only 17 percent said they should be allowed to become legal permanent residents but not citizens. An even smaller number, 10 percent, said they should be deported.

In June, the Senate passed a broad immigration bill that includes a path to citizenship for all of an estimated 11.7 million immigrants here illegally. Republican leaders in the House said they would not take up that measure but that they could act on smaller bills that would strengthen enforcement and make other fixes to the system. Some Republicans have said they would consider legal status for illegal immigrants, but without any path to citizenship.

Half of Hispanic adults are immigrants born outside the United States. But in contrast to widespread perceptions that many Latinos are here illegally and do not speak English well, the report cites census data showing that two-thirds of Hispanic adults are U.S citizens and about two-thirds either speak English primarily or are bilingual.

The poll was conducted between Aug. 23 and Sept. 3 and was released at a conference of religion news writers in Austin. Online interviews were conducted in English and Spanish with 1,563 Hispanic adults, citizens and noncitizens, who were part of the GfK KnowledgePanel, a nationally representative probability sample of Americans, and the margin of sampling error is plus or minus 4 percentage points.