With the earnings from her job in a Houston hair salon, Ms. Martínez, 30, is supporting one child born in Texas and three others she left behind in her home country, Nicaragua.
“So many people back there depend on those of us who are here,” she said. “It would be such a help if we could work in peace and go back sometimes to see our children.”
As President Obama looks for a way to salvage a broad overhaul of the immigration system, he opened the door this week to a piecemeal series of smaller bills as a way of getting past the objections of the Republican-run House, which refused to take up the comprehensive measure that the Senate passed in June.
But as far as Ms. Martínez and many other immigrants are concerned, one of House Republicans’ sharpest disagreements with the Senate and the White House, over a path to citizenship for those here illegally, should not be that hard to resolve.
“For many undocumented people, citizenship is not a priority,” said Oscar A. Chacon, executive director of the National Alliance of Latin American and Caribbean Communities, a network of immigrant organizations that includes many foreigners here without papers. “What they really care about is a solution that allows them to overcome their greatest vulnerabilities.”
The Senate bill includes a 13-year pathway for 11.7 million illegal immigrants that ends with a chance to naturalize. President Obama and other supporters of that measure insist that any alternative would create a disenfranchised underclass. Many House Republicans reject the Senate path as rewarding immigrants who broke the law. But a growing number of Republicans say they remain ready to work on immigration and could consider legalization, if it did not involve any direct route to citizenship.
For foreigners like Ms. Martínez — those who cannot get a driver’s license in most states and live with gnawing worry about being fired or deported — that would be enough. They aspire to become Americans, they said in phone interviews, but would settle for less if they could work and drive legally, and visit relatives outside the country.
Another woman in Houston, Elena Sandoval, described a painful moment when her father died in El Salvador and she could not attend his funeral knowing she would not get back into the United States. Ms. Sandoval, 48, a house cleaner, sends money home for her three children.
“I can’t tell you how hard it is to leave your family,” Ms. Sandoval said with a sigh. “If only I could have permission to move about freely,” she added. “Citizenship would just be a blessing we would pray for.”
Most groups working for immigrant rights vehemently oppose any legislation that would deny millions of people the opportunity for full equality.
“We either have a path to citizenship or a path to hell,” said María Rodriguez, executive director of the Florida Immigrant Coalition. “To codify a person who lives in this country but will never have an opportunity for citizenship creates a second class. It seems completely un-American.”
Advocates say the Senate’s path — which requires illegal immigrants to pay fines and back taxes, study English, pass criminal checks and wait in line behind foreigners who applied legally — is sufficiently long and arduous. This month there have been rallies and protests nationwide and a fast on the National Mall to pressure the House to vote on a bill with citizenship.
But among immigrants there is no consensus. In South Florida, there were anguished discussions over café con leche and empanadas among members of Dreamers’ Moms, a group of mothers of young immigrants who have joined the movement.
“Citizenship is fundamental,” insists Yaquelín López, 46, a Bolivian who has been in the United States illegally for a decade. “Otherwise we will be 11 million people left in limbo.”
Marcela Espinal agrees.
“We have been working hard for our families and paying taxes all these years and we never lived off the government,” said Ms. Espinal, 35, a Honduran employed for more than a decade in construction. “Why shouldn’t we be able to vote someday?”
Ashley Parker contributed reporting.