“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.”

Democrats in Congress and President Obama have signaled a willingness to listen to an emerging House GOP proposal, which would offer limited legal status. At the same time, Richard L. Trumka, president of the AFL-CIO, the nation’s largest labor union, said such a plan would be a “nonstarter” and would not receive union backing.

Frank Sharry, executive director of the immigrant advocacy group America’s Voice, said neither advocates or Democratic legislators would accept proposals that “create a permanent underclass” of noncitizens, but that they might accept legislation that allowed many undocumented immigrants to obtain some form of legal status and “most, if not all” to achieve citizenship through “normal channels.”

“The details matter hugely, and we don’t know what they will be,” Sharry said. But if ideas being discussed among Republicans evolve into concrete proposals, including citizenship for student “Dreamers,” work permits for some adults, and green card sponsorship for spouses and parents of U.S. citizens, he said, “that might meet our demands.”

According to a study released this month by the National Foundation for American Policy in Arlington, between 4.4 million and 6.5­­ million illegal immigrants — mostly parents of U.S.-born children — could gain eventual U.S. residency under approaches being discussed informally in the House. The bipartisan Senate bill that passed last year would have allowed about 8 million people to gain residency.

While the new flexibility among House Republicans on immigration reform largely reflects a pragmatic realization that they will need to attract the rapidly growing number of Latinos and immigrant voters, the less adamant insistence on citizenship among immigration advocates reflects a more practical attitude among many undocumented immigrants themselves.

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 for illegal immigrants than having a pathway to citizenship. The report said that 59 percent of foreign-born Hispanics expressed fear that they, a relative or close friend might be deported. Pew called these findings a potential “opening for legislative compromise. “

The study found that 55 percent of Hispanics, a group that accounts for three-quarters of unauthorized immigrants in the United States, see legal protection as a higher priority than citizenship. It 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.

In interviews this week in the Washington area, a variety of undocumented immigrants expressed similar views to the Pew survey, calling citizenship a distant dream that paled in comparison with their urgent desire to be able to work legally and without fear.

“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 who lives 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.”

Adrian Maldonado, 57, an undocumented immigrant from Mexico who was looking for a day-labor job in Annandale, Va., last week, said that he had entered the United States numerous times to do construction work, but that he always returned to his family.

“For me, the absolute priority is to work,” he said. “I know some American people don’t like us being here, but if you are honorable and do not go into the streets and steal and drink, you deserve to be allowed to work. It would be beautiful to be a citizen, but what is more beneficial to me is a work permit. I ask nothing more of this country.”

Immigration advocates said there were a number of ways illegal immigrants could be given legal status that could lead to citizenship under certain circumstances, such as sponsorship by employers or relatives, but that would not automatically offer them that chance. It is the notion of such an automatic offer, or “special path,” that has aroused such ardent opposition among many House Republicans.

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 by advocates Wednesday, she described one area of compromise that legislators could pursue.

“Congress could create a program where people who meet certain requirements and qualifications 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 naturalize and become a citizen.”

The two other major categories of immigrants who could be legalized through legislative compromise, in many cases by expanding or modifying legal channels that exist, are those who were brought here as children, known as “Dreamers,” and parents or spouses of U.S. citizens.

According to the study by the National Foundation for American Policy, between 800,000 and 1.5 million immigrants are Dreamers who came to the United States illegally as children, and at least an additional 4 million are undocumented parents or spouses of U.S. citizens. Congress could conceivably grant such individuals the right to be sponsored for residency by their citizen relatives, and it could remove multi-year legal barriers for them to return to the country if deported.

“If the 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, a former federal immigration official and the author of the study.

Obama has ordered a legal amnesty for qualified members of the Dreamer generation who arrived in the United States before they turned 16, but some advocates said it should be expanded to include slightly older people as well.

“If Republicans are saying that citizenship is okay for some people under some conditions but not for everyone, then it raises an immediate question,” said Gustavo Andrade, who works with young immigrants at the advocacy group CASA of Maryland. “If someone now aged 29 can qualify for citizenship, why not someone aged 32?” he asked. “How do you decide who is deserving and who isn’t?”