Angeles P. Barberena has always tried to follow the United States’ immigration laws. She dutifully filed her petition to become a resident, complied with the requirements and paid her taxes and fees.

That was 17 years ago. Barberena, who is from Mexico, is still waiting. Her file is inching through a backlog, and she has several years to go before she will receive the green card that will make her a permanent resident.

As Congress debates an overhaul of the immigration system, Barberena often feels like yelling with frustration. "It’s been so long and we did everything by the rule," she said, speaking from her home near Nashville, Tenn. "Now it seems everything is about illegal immigrants and nothing is about us."

While stark differences between the Senate and the Republican-controlled House of Representatives have centered on border security and a pathway to citizenship for immigrants here illegally, another major issue is snagged in the dispute: the plight of more than 4.4 million legal immigrants like Barberena who are languishing in a broken system.

A broad bill the Senate passed in June includes ambitious measures to eliminate green card backlogs and create a new merit program, based mainly on education and job skills, to expand and streamline future legal immigration. House Republicans have made it clear they will not take up that bill. Instead, Speaker John A. Boehner said the House would handle immigration in "bite-size chunks" over the coming months.

None of several smaller measures recently approved by House committees deal with fixing the visa system, and a bipartisan House bill similar to the Senate’s has stalled. For many House conservatives, the increase in legal immigration under the Senate plan is nearly as objectionable as the promise of citizenship for immigrants here illegally.

As the overhaul becomes uncertain, so do the prospects of Eduardo de Souza, a college soccer coach from Brazil working in Virginia who has, like Barberena, been waiting more than a decade to become a permanent resident.

"What is the government going to do for those people who are doing the right thing?" de Souza asked.

The backlogs swelled because of a long-standing mismatch in immigration law between the number of visas available and the much larger number of foreigners who qualify for them, especially those applying based on family ties to U.S. citizens and permanent residents. Congress has imposed caps on the number of visas issued to each country each year.

As a result, immigrants from some countries — particularly China, India, Mexico and the Philippines — can wait a decade or more to get their visas after approvals. Most foreigners are waiting outside the United States, but many — at least hundreds of thousands — live here on temporary visas or work permits.

The 1,192 pages of the Senate bill include a little-noticed requirement, or "trigger," linked to the visa logjam: All backlogs of legal applicants must be cleared within 10 years before any immigrants who had been here illegally can obtain green cards, the pivotal step toward citizenship.

To accomplish that, any foreigners like Barberena who have been waiting more than five years for green cards would become eligible for visas immediately. The immigration authorities would devise a formula to issue visas for everyone in line over seven years, giving priority to those who waited longest. Under the Senate plan, Barberena could receive her green card within months.

The legislation would also free up visas by removing numerical caps for spouses and children of permanent residents, and by closing down some other family categories. But over time the merit system would offer an even greater number of new green cards, particularly for highly skilled foreigners and for low-wage laborers.

All in all, the Senate provisions would expand the immigration system and bring a rapid influx of legal immigrants, increasing the foreign-born share of the population to 15 percent by 2020, according to Steven A. Camarota, director of research at the Center for Immigration Studies in Washington. That would be a fivefold increase since 1970 and the highest percentage of immigrants in the nation’s history, said Camarota, whose group advocates reducing immigration.

At a rally Monday in Washington, Rep. Mo Brooks, R-Ala., a vigorous opponent of the overhaul, posed a question to the largely conservative crowd: "What is the impact of these huge numbers the Senate bill wants to foist upon the American people?" he asked. "You’re going to have a huge influx of people who are competing for jobs," he said, referring to new legal immigrants and undocumented immigrants who would gain legal status. "These are American jobs for American citizens."

Barberena has not had time to study the details of the proposals before Congress. She is working to keep her family afloat in a job with irregular hours at an upscale food market in a Nashville suburb.

A supermarket is not where Barberena, 56, thought she would be at this stage in life. After completing undergraduate studies in chemical engineering at one of Mexico’s best universities, she led a comfortable middle-class life in Mexico City.

But she left in 1995 with her husband, two small sons and a sense of desperation. A neighbor’s daughter had been abducted, bringing an epidemic of kidnappings within reach of her own family.

"I lived in panic because I did not have any way to protect my children," Barberena said.

In 1996, her father, a naturalized American citizen, presented a green card petition for Barberena, his married adult child. And the wait began.

Barberena regularly checked a State Department bulletin that advises applicants when they can expect their visas. As of this month, the authorities are issuing visas to Mexicans in Barberena’s category who applied three years before she did: in 1993.

"No wonder my nerves are shot," she said.

Over the years Barberena scrambled to maintain her legal status and help support her family. She carefully updated her sons’ student visas, paying full tuition at the foreign student rate for one son at Northeastern University in Boston. At one point, on the advice of lawyers, she and her husband obtained visas by investing in several U.S. businesses, including ownership of a Tennessee dealership that sold therapeutic saunas. That enterprise faltered because of manufacturing problems, and by 2011 they had lost the business and the visas. Now they have valid work permits. "The immigration system is just absolutely broken," Barberena said with a sigh. "But I would do it all again. I lost certain social status I had in Mexico, a nice rhythm of life, but I don’t care. I am telling you, we love this country."

But before Congress gives any help to illegal immigrants, Barberena said, she wants her family to become citizens first.

De Souza agrees. He played soccer professionally in Brazil, and first came to the United States in 1999. Since then he has completed a master’s degree in education and worked his way up to become associate head coach at Longwood University, a state institution in Virginia. In 2011, two years after he started there, the men’s soccer team won its conference championship.

In the summer he teaches soccer camp with an ambition to train more young athletes so they will take up his game. With his last temporary visa set to expire in 2015, the university is helping him apply for permanent residency based on his professional skills, but his wait could be many more years. Under the Senate bill, De Souza would get his green card immediately — if a similar measure is approved by the House.

"I have been doing it legally all the way, just what a regular American citizen would do," De Souza said. But, he added, "I don’t see any advantage for the legal immigrant right now."

© 2013 The New York Times Company