During a news conference on the annual House Republican retreat, Speaker of the House John Boehner said members would be hammering out principles going forward for immigration reform. (The Washington Post)

Many advocates for immigrants, responding positively to new Republican overtures on immigration reform, are signaling they may back off on their longtime insistence that legislation must include a “special path” to citizenship for the country’s estimated 11 million illegal immigrants.

Instead, a variety of advocate groups said they were delighted that House GOP leaders are seeking ways to compromise on the topic, including proposals that could legalize many undocumented immigrants but not necessarily allow them all to become U.S. citizens.

On Thursday, House Speaker John A. Boehner (R-Ohio) released a list of Republican “principles” on immigration. The statement declared that there would be “no special path” to citizenship for illegal immigrants, but that, in general, they should be allowed to “live legally and without fear” in the United States if they meet a list of tough requirements and rules.

Tamar Jacoby, head of the Washington-based advocacy group ImmigrationWorks USA, called the Republican statement on legalizing undocumented immigrants a “historic breakthrough” and a “critical first step” to meaningful immigration reform. The principles did not include any specific policy proposals or time line.

Some labor unions and immigrant groups said they would continue to insist on a full path to citizenship, and some conservative Republicans said they would fight against legalizing undocumented immigrants, which they call an “amnesty” for lawbreakers. But Boehner’s statement seemed to signal a sea change in the party’s stance, and many major immigrant advocate groups seemed eager to respond in kind.

“To see the Republicans moving from self-deportation to legalization is a major shift,” said Clarissa Martinez of the National Council of La Raza in Washington. “There is a big chasm between saying ‘no special path’ and shutting the door to citizenship entirely. It could mean a lot of things. There is no clarity or definition yet, but it is a start and we are definitely encouraged.”

Frank Sharry, executive director of the advocacy group America’s Voice, said his group and most Democrats oppose creating a “permanent underclass” of noncitizens. But he said they might accept legislation that allows many immigrants — including workers, youths and immediate relatives of U.S. citizens — to obtain some form of legal status and “most” of them to achieve citizenship through “normal channels.”

According to a study by the National Foundation for American Policy in Arlington, 4.4 million to 6.5­­ million illegal immigrants could gain eventual U.S. residency under approaches being discussed informally in the House. The bipartisan Senate bill on immigration that passed last year would have allowed about 8 million people to gain residency.

While the new flexibility among House Republicans reflects a realization that they need to attract the rapidly growing number of Latinos and immigrant voters, the softening of demands by immigration advocates reflects the practical attitudes of many undocumented immigrants.

According to a recent study by the Pew Hispanic Center, a majority of Hispanics in the United States believe that being able to live and work in the country legally, without fear of being deported, is more important than having a pathway to citizenship. The study said 59 percent of foreign-born immigrants expressed fear that they or those close to them could be deported.

Pew also noted that many immigrants do not choose to seek citizenship when they have the opportunity and that only 44 percent of legal Hispanic immigrants have become citizens. It said these findings signaled a potential “opening for legislative compromise” on legalization.

In interviews this week, a variety of undocumented immigrants in the Washington area expressed similar views to the Pew survey, saying they were far more interested in being able to work legally than in eventually becoming an American citizen.

“Why do we have all these marches and speeches about citizenship for 10 million people? Why don’t they focus on what we all want, which is to be able to work?” said Jose Joya, 36, a maintenance worker from El Salvador in the District. “If you get a work permit, you can buy a car and pay your taxes and spend money without thinking you could be arrested. What we want is to be legal.”

Immigration advocates said there were a number of ways illegal immigrants could be given legal status that might lead to citizenship under certain circumstances, such as sponsorship by employers or relatives.

Angela Kelley, an immigration expert at the Center for American Progress, said the “palpable political thaw” among Republicans was creating “balmy conditions” for compromise. In a telephone news conference Wednesday, she described one such policy that legislators could pursue.

“Congress could create a program where people who meet certain requirements can get work authorization that permits them to be in the U.S. for a period of time, and then renew it, and be protected from deportation,” Kelley said. “It would permit you to travel, but not give you status like a green card that you could adjust to . . . become a citizen.”

The other major group of people who could be legalized are the estimated 4 million undocumented parents or spouses of U.S. citizens. Congress could conceivably grant them the right to be sponsored for residency by their relatives and remove multi-year legal barriers for them to return to the country if deported.

A third group is the 800,000 to 1.5 million people known as “dreamers” who entered the U.S. illegally as children. President Obama has already granted many of them the right to seek legal residency, and House Republican leaders Thursday signaled support for their legalization and eventual citizenship.

“If Republican proposals are generous with the dreamers, offer people without criminal problems a chance to stay and work, and allow those with close family members or jobs to be sponsored for green cards, then it would be realistic to have a compromise with the Senate position,” said Stuart Anderson, an analyst and former federal immigration official.