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With presidential contenders on all sides struggling to refine their positions on the prickly issue of immigration, nearly three-quarters of Americans say they support a pathway to legal status for undocumented immigrants, according to a poll published Thursday by the Pew Research Center.

In the survey, 72 percent of Americans said immigrants here illegally should be allowed to stay if they meet some requirements, results that have varied little over the last two years. They included 42 percent of Americans who say those immigrants should be allowed to become citizens and 26 percent who say they should only become permanent residents.

Among Republicans, a majority of those questioned — 56 percent — supports a path to legal status for undocumented immigrants. Republicans are generally critical of their party’s performance on illegal immigration, with 59 percent saying the party is not doing a good job representing their views on how to deal with illegal immigration.

In Congress and among the large field of presidential contenders, many Republicans have moved right on the issue, rejecting legalization and calling for tougher enforcement and border security.

According to the Pew poll, a majority of Americans — 58 percent — reject the idea that allowing undocumented immigrants to gain legal status is rewarding them for “doing something wrong.”

Among Hispanics, a fast-growing electorate that candidates from both parties are courting, 86 percent say there should be a path to legal status, with 54 percent of Hispanics saying undocumented immigrants should be allowed to become citizens.

Democrats also overwhelmingly support legal status, with 80 percent saying those immigrants should be allowed to stay if they meet requirements.

President Obama’s ratings have plunged on immigration, with 56 percent of Americans in the survey saying they disapprove of his handling of the issue and 37 percent saying they approve. Hispanics, who have long supported the president, are now evenly divided, with 48 percent disapproving of his performance and 44 percent approving.

In November, Mr. Obama announced that he would give protection from deportation and work permits to more than four million undocumented immigrants. Texas and 25 other states brought a lawsuit to stop the programs, blocking them in the federal courts.