Lincoln Diaz-Balart doesn’t need permission to drop in on his hometown congressman. He knocks and strolls into the Capitol Hill office.

“Just wanted to pop my head in to say hi,” he says, taking a seat. Lincoln isn’t a typical constituent. He’s Rep. Mario Diaz-Balart’s elder brother.

Mario — a Republican from the Miami area — hugs his brother and tells him it’s good to see him. Such visits are rare since Lincoln left Congress in 2011. Lincoln has the longer hair and wider face of an elder statesman, but you can tell they are brothers by their eyes. All four of the Diaz-Balart brothers, known to some as the Cuban Kennedys, have eyes that look like they’re pinching the bridges of their noses.

“Nobody can deny that our immigration system is broken,” says Mario, returning to an interview with a reporter and to the topic that he has worked as hard on as any other House Republican. “Ignoring that is like trying to block the sun with your thumb. You can do that for a second, but we’ve been doing it forever.”

As Mario speaks, Lincoln gets up to retrieve a framed photograph from the windowsill. It’s from 1997, a crowd of beaming Nicaraguans hoisting Lincoln into the air to celebrate the passage of his bill to help legalize thousands of undocumented Central Americans living in the United States.

“This is the most emotionally impactful moment of my time in Congress,” says Lincoln in his sonorous voice, patting his chest with his hand. For the past year, a Ralph Waldo Emerson quote has been weighing down Lincoln’s breast pocket. “To know even one life has breathed easier because you have lived,” it reads, “this is to have succeeded.”

But major success, the kind that could have made it easier to breathe for millions of undocumented citizens, has been more elusive. For the Diaz-Balarts, dealing with the issue is practically the family business.

Lincoln, 59, spent 18 years in Congress, helping organize a bipartisan group of lawmakers that met to draft legislation. Today, Mario, 52, has taken on a lead role in a Republican conference that can’t quite figure out how to handle the issue. A third brother, Jose, has the role of documenting the whole thing. His job as the lead anchor of the Spanish-language channel Telemundo has him speaking about the issue on television to millions of viewers each week. Just last week, Jose, 53, sat down with President Obama for a testy interview about the president’s struggling reputation among Latino voters.

As exiles forced from their home in Cuba, nobody can say that the Diaz-Balarts didn’t go through difficulties with immigration. But they are products of a generous policy that allowed hundreds of thousands of Cubans to live in the United States in the 1960s and ’70s. These days, the brothers are bringing to the forefront the fact that millions of others haven’t been given the same easy passage that their family enjoyed.

Despite all the work and all the coverage, immigration reform is unlikely anytime soon. This can be seen as a failure of Congress as a whole or of Republicans in the House. Some also see it as Mario’s failure, as well.

“Whatever his personal feelings may be, it’s clear that he has no influence,” says Fernando Espuelas, a radio host for the Univision America Network. “I think it’s an issue of ‘Does he make a difference? Does he have some sort of capacity to bring along or construct a majority?’ And it’s obvious he does not.”

But for the Diaz-Balarts, who have been going through their own forms of tragedy over the past few years, it’s a fight they can’t pass up.

“You’ve got families that are every day being broken up,” Mario says, looking at Lincoln. “You can’t just pretend that’s not the case.”

* * *

Before Rafael Diaz-Balart — the patriarch of the family — became the chief critic of Fidel Castro, he was Fidel’s brother-in-law. The two attended school together in Cuba and were close for a time, and Castro married Rafael’s sister, Mirta.

The friendship didn’t last (and neither did the marriage). As Rafael grew into his political awareness, becoming the majority leader of the Cuban House of Representatives and the undersecretary of the interior under Castro’s predecessor, President Fulgencio Batista, he became one of Castro’s chief critics.

In 1955, as the House considered giving amnesty to Castro for his role in an attack two years earlier, Rafael stood on the House floor to declare, “Fidel Castro is nothing more than a psychopathic fascist.”

Rafael’s two oldest sons, Rafa, 63 — an investment banker who lives in Miami — and Lincoln — who started his own law firm and consulting business after leaving Congress — were born in Cuba during this time. Today, they work out of the same office on the Miami waterfront.

“I don’t have fond memories of being in Cuba,” Rafa says over lunch with his brother. “My father was probably the most vociferous enemy of Castro. This made us the target of violence. We had to go to school with bodyguards. It meant we had lots of friends in school, but no friends who could come home with us.”

When Rafa was 8 and Lincoln 4, the family left on a trip that was supposed to last a few weeks. But while they were in Spain, Castro took over the island, and the family never had the chance to return. Rafael moved the family to the United States, where his two youngest sons, Jose and Mario, would be born. He was fond of saying his boys were “100 percent American and 100 percent Cuban.”

The brothers see themselves that way, too, as a family of immigrants. It gives them empathy, they say.

“Something has to be done to not have fifth-class citizens in the country that calls itself the most democratic, the most humane country in the world,” Rafa says, cutting into his veal cutlet.

Lincoln interrupts. “The country that is the most democratic,” he says, watching as his fish entree is deboned. “We receive a million legal immigrants a year. No other country in the world does that.”

“I know,” Rafa says, “but we have to solve that issue.”

Always a tight-knit group, the family has been torn up over the past few years, although not by the government.

In 2005, the Diaz-Balart brothers lost their father; their mother died last year. And this past May 19, Lincoln’s 29-year-old son, Lincoln Gabriel (known as LG), took his life after years of battling depression. Sometime before he died, LG grabbed a pen and wrote out the quote from Emerson that Lincoln carries. The author had been LG’s great-grandmother’s favorite writer: She named one son Rafael and another Waldo.

“If one life breathes easier because of what you’ve done, you’ve succeeded,” Lincoln says, pulling the note out of his pocket at lunch. “That’s public service. I was in Northern California back in March, at a hotel restaurant. A gentleman brought his daughter and said [to her], ‘I want you to meet the person that made you an American citizen.’ That’s very touching.” Immigration reform is a topic Lincoln continues to be passionate about.

* * *

Before the 1980s, before they fell in love with Ronald Reagan, Mario and Lincoln were Democrats. But they don’t sound like liberals, even when they talk about helping undocumented immigrants obtain legal status. Mario refrains from using the term “legalization” publicly, knowing that it could scare away many of his colleagues.

“I think people look to Mario as an honest broker and one who understands the conservative Republican position on the issue,” says Rep. Paul Ryan (R-Wis.), the former vice presidential nominee who has expressed interest in immigration reform. “He’s obviously been tapped by [Speaker John A. Boehner] to play a lead role.”

Not everyone is thrilled with the results. Mario says there are days when two sets of protests take place outside his home, one from the left and another from the right. Espuelas, the Univision radio host, sees Mario as just a pawn to be “used by Republicans to deliver messages.”

The reality is, Mario is playing an inside game. Republicans in the House have to worry about getting a primary challenge on the right if they appear soft on immigration, and conservative groups such as the Heritage Foundation say no legislation is the best course of action this year.

“Do we really think that the left is content to stop with only a half loaf?” Derrick Morgan, a vice president of the Heritage Foundation said in a speech last week, referring to Republican plans that would grant legal status but not citizenship to many undocumented immigrants. “I think it’s far more likely that before the ink on President Obama’s signature on the law has dried, that the left will decry the ‘Jim Crow’ status of these newly legalized immigrants.”

* * *

Hialeah, in Greater Miami, is home to the most Cubans per capita, about 200,000 fluent Spanish speakers and an old shoe factory that now functions as the headquarters of the television station Telemundo.

The host of a live show every weeknight and a pre-taped Sunday show, Jose works in an office scattered with reminders of his 30 years in journalism: framed photographs from his time as a host on CBS’s “This Morning,” a string of bullet casings from his time as a war correspondent in El Salvador, a badge that recognizes him as a three-second champion from an attempt at bull riding for a TV segment, a photo of one of his nine interviews with Obama.

Jose looks the most like Mario, but with a fuller head of hair. “Whenever I go on with Jose, I tell Mario, ‘You have anything you want me to tell your taller, better-looking brother?’ ” says Rep. Luis V. Gutierrez, a regular guest on Jose’s show.

Both Jose and Mario probably speak with Gutierrez, a Democrat from the Chicago area and a leading voice on immigration from the left, more than they speak with each other. After a recent taping, Gutierrez told Jose he was going to be in Miami for an event with Mario in the coming weeks.

“I was like, ‘Let’s find out what the story is on that,’ ” Jose tells me afterward. “My brother would never think of telling me. I get his press releases.”

To avoid a conflict of interest, Jose won’t interview his brothers.

Lincoln, who used to put on boxing gloves when he was 14 and whale on Jose, says he respects the decision. But he also notes that he saw Chris Cuomo on CNN interview his brother, New York Gov. Andrew Cuomo (D).

Jose, who remembers intentionally busting his elder brother’s drum set as some kind of payback, refrained from comparing Lincoln to Andrew Cuomo and said interviewing family would just make him part of the story.

“Maybe one day, when we are both retired from our jobs, I could in a public forum interview Lincoln and get some of these issues that he clearly has out into the open,” Jose says.

Jose talks about immigration reform the same way he talks about covering a war, changes in health care or a natural disaster: as a story. It just happens to be the biggest issue for his viewership.

“If I can even one time get someone who doesn’t understand the reality of someone else to say, ‘There but for the grace of God go I,’ then I’ve done my job,” he says. The lessons from his father about the importance of service, the same lessons that resonate with his brothers and that clearly meant something to his nephew Lincoln Gabriel, matter to him as well.

At the end of our interview, he pulls out his iPad to play something he says he doesn’t share with others. It’s the last time he heard his father’s voice, left for him on his answering machine.

“Jose, it’s your father. Call me because I want to exchange some ideas with you,” he says in Spanish. “And a hug.”

To Jose, that was his father in a nutshell.

“I miss that about him,” Jose says. “I miss that he said, ‘What are you reading, and are you making a difference?’ ”