El Paso, Texas (CNN) Rubén Lorenzo Peláez circles the chair like a ninja, silently shifting from one foot to the other.

For a moment, the snip-snip-snip of his shears is the only sound in the room.

The scissors won't close all the way. His vision is blurry. And he's nearly 2,000 miles away from the loyal clients who once got bobs and buzz cuts at his barber shop in central Cuba.

But this is the first time in months he's felt at home.

It's been just a day since Lorenzo sat in an airplane's aisle seat, shaping his thumb and index finger into an "L" for "libertad" as a friend snapped his photo.

The chartered jet was one of dozens that shuttled stranded Cuban migrants from Panama to Mexico this month in what officials described as a humanitarian airlift.

Its aim: help Cubans reach the United States after several Central American countries closed their borders to the surge of people pushing north.

Lorenzo made it onto the last flight.

Now he -- and thousands of others who say they're fleeing a repressive government and searching for economic opportunity -- are taking their first steps in the United States.

As America's newest immigrants search for places to put down roots, refugee agencies say they're struggling to deal with the influx, and politicians are sparring over whether this group of immigrants should be here in the first place.

It's a familiar refrain, but one with a twist: Because they're Cuban, these immigrants are in the United States legally the second they arrive, regardless of how they get here. And unlike the Central Americans who've flooded across the border in recent years, they have little reason to fear deportation.

Lorenzo, 47, has been sleeping in a church pew since his arrival in Texas. And the bald and bespectacled barber says he's not going anywhere.

"Here," he says, "is where I'm staying."

Yadira Lozano Odio is overcome with emotion thinking of friends she left behind in Cuba.

Risks and rewards

Families sleep on rows of cots that stretch wall to wall in a community center gym. New arrivals rifle through boxes of used clothing, searching for something that might fit. A little girl looks shocked as a volunteer hands her two Barbies.

Alianise Valle Paloma, 10, smiles as she tugs on one doll's yellow shirt and runs her fingers through its brown hair.

"We haven't had toys for years," says her mother, Yadira Paloma Fombellida.

In Cuba, she says, the family of four struggled to make ends meet. So they, like many Cubans, left for the promise of a better life in Ecuador, where they wouldn't need a visa to enter the country. But the family's efforts to make a living there didn't work out.

"They didn't pay us. ... It was worse than Cuba," says Paloma's husband, Julio Cesar Valle Hernandez.

That's a common thread in many of the stories shared by Cubans streaming into church-run shelters in El Paso, where they swap details of their harrowing journeys north:

The financial hardships they faced in Cuba. The low wages they earned working as undocumented immigrants in Ecuador. The South American country's threats to deport them. The dangers of hiking for days through the Colombian jungle, facing rough terrain, armed groups and extortion by authorities. The fear they'd never make it out of Panama, where many of them were stranded for months after Nicaragua and Costa Rica closed their borders.

Experts say several factors are fueling a spike in the number of Cubans to brave this dangerous journey to reach the United States. Chief among them: fear that U.S. policies that put Cubans on a fast track to legal residency could be repealed as relations between the two countries improve.

For El Paso residents who've stepped up to help the arriving immigrants, the conversations have been eye-opening.

"It's been a roller coaster," says Veronica Román, executive director of the Houchen Community Center, the first stop for more than 1,700 Cubans who arrived in the past few weeks. "It's a lot of mixed emotions when you hear their stories. ... You say, 'Wow, I'm taking my freedom for granted.'"

As his daughter plays with her Barbies, Valle says the journey to the United States was far more difficult than he'd expected. But the trip was worth it, he says, to give his children a future.

And still, he says, it was better than what his brother went through, trying to leave Cuba on a boat -- only to find himself stranded at sea for five days on a rickety raft, rescued by the Coast Guard and deported back.

"At least in the mountains," Valle says, "there is earth under your feet."

Photos: What they brought Yordanis Garcia Milian, 28, knew he couldn't leave Cuba without a snapshot from his surprise 15th birthday party. The photo shows his parents smiling that day. "This memory, wherever I am, will go with me, because I can lose everything, but not the hope of fighting for them and fighting to have them here with me," he said. Milian is one of more than 3,000 Cubans who flew from Panama to Mexico and crossed into the United States in May. Here's a look at some of the things they carried with them. Hide Caption 1 of 7 Photos: What they brought "When she gave me the bear, she told me she would always be with me," Yadira Lozano Odio, 31, said, her eyes welling up with tears as she described the moment she said goodbye to her best friend in Santiago de Cuba. Lozano keeps a necklace wrapped around the small stuffed panda -- a gift from another close friend. The necklace, she said, was blessed by a priest in her friend's church. Hide Caption 2 of 7 Photos: What they brought Osdaisy Calaña Bujol, 31, wore a necklace her 8-year-old son made for her before she left Cuba. He told her it would bring her good luck. "It's already green," she said, "but it's the most important thing I have." Hide Caption 3 of 7 Photos: What they brought Wrapped in clothes in a backpack he carried from Ecuador to the United States, Julio Cesar Valle Hernandez keeps small statues of the Virgen de la Regla (Our Lady of Regla) and San Lazaro (Saint Lazarus). "It got broken on the way," he said, "but I couldn't leave it behind." Hide Caption 4 of 7 Photos: What they brought It's heavy, but Angel Bornell Batista, 27, didn't think twice about packing a sacred Eleguá stone when she left Cuba a year ago, or bringing it along on the three-month journey from Ecuador to the United States. "I asked him to clear the path for me," Bornell said. Hide Caption 5 of 7 Photos: What they brought Edgardo Nuñez Cobas, 43, used to work as a cook at a five-star hotel in Cuba. He brought a certificate that shows his hospitality training with him to the United States and hopes it will help him land a job. For now, days after he arrived in America, he's cooking food at a shelter where Cubans who've just crossed into the United States are staying in El Paso, Texas. Hide Caption 6 of 7 Photos: What they brought Nuñez also brought a beaded necklace with him that he's had since he was 18 years old. Hide Caption 7 of 7

An unlikely location

As Lorenzo sweeps the floor, the Rev. Karl Heimer leans back in the church office chair that's become the center of a makeshift barbershop. He doesn't have much hair left, but the Cuban barber has found a way to trim it.

"How do I look?" the 75-year-old pastor asks him. "Can't you add a little hair on the top?"

Heimer has spent decades working at this Lutheran mission less than a mile from the U.S.-Mexico border.

He brings Bibles to jailed Central American and Mexican immigrants and hosts mission groups who build houses just across the border in Ciudad Juarez.

"Never did I think I'd be helping my own people," says Heimer. The pastor left his home in Guantánamo, Cuba, in the 1950s to study in the United States; after Fidel Castro came to power, Heimer applied for refugee status.

Now, the mission he runs has become a shelter for dozens of Cubans who've just arrived in El Paso and have nowhere else to go.

"I'm loving it, (but) it makes me feel like crying sometimes, because of my mother," Heimer says. A proud Cuban from the coastal city of Cienfuegos, she came to the United States in the early 1960s and lived with him in Texas before she died in 1997. He knows she would have gotten a kick out of the arrival of so many Cubans in such an unlikely place. "The sad thing about it is she couldn't be here to see it."

For many years, it would have been unthinkable to see a wave of Cuban immigrants walking across pedestrian border bridges that stretch across the Rio Grande and into this land-locked city.

But times have changed. While the U.S. Coast Guard says it has seen a spike in the number of Cubans trying to reach the United States on boats, far more are coming to the country on land.

More than 35,600 Cubans have arrived at U.S. ports of entry since October 1, nearly three-quarters of them at the Texas border, according to U.S. figures.

More than 4,700 crossed in El Paso alone, according to a CNN tally using numbers from U.S. and Mexican immigration officials.

And the numbers show no sign of slowing.

It's a blessing, Heimer says, to have so many skilled immigrants arriving. Lawyers, doctors and engineers are among the Cubans who made it to Texas this month.

"They will add to our society," Heimer says.

The Rev. Karl Heimer left Cuba for the United States in the 1950s; the recent wave of migrants has taken him by surprise.

Washington weighs in

The papers stapled into their passports are stamped with words that give Cubans a leg up the second they step foot in the United States: "Paroled to pursue adjustment of status under public law 89-732."

While immigrants from other countries seeking asylum in the United States often struggle to make their case in court, Cubans don't have to jump over the same hurdles. The Cuban Adjustment Act, passed in 1966, gives any Cuban who sets foot in the United States permission to enter. After a year and a day in the country , they're eligible to apply for a green card.

Other government policies grant them benefits like food stamps, Medicaid, housing assistance and work permits soon after their arrival.

Snapshot: Cuban migration Prompted in part by fears that thawing relations with Cuba will end favorable U.S. policies, thousands of Cuban immigrants are trekking through Latin America on their way to the United States. Here's a snapshot of other countries involved: Ecuador was once a magnet for Cuban migrants because the South American country didn't require entry visas. That practice ended last year, and many Cubans are leaving with the threat of deportation looming. Nicaragua in Central America closed its border to Cubans heading north last year, leaving thousands stranded to the south in Costa Rica. Costa Rica struck a deal in January to begin airlifting Cubans out of the country, then closed its borders to stop more from coming in. That left thousands stranded to the south in Panama. Panama began humanitarian airlifts this month that sent more than 3,100 stranded Cubans north to Mexico at the U.S. border. Now Panama's borders are closed, too. Mexico gives Cubans arriving on flights from Central America temporary papers and shuttles them to the U.S. border.

In recent months, a number of U.S. lawmakers have slammed the Cuban Adjustment Act, claiming it gives Cubans an unfair advantage and allows scammers to exploit the system.

"There's no logical reason to give preference to Cubans over immigrants from other countries around the world. ... The Cold War is over. We're normalizing relations with Cuba," says Rep. Beto O'Rourke, a Democrat who represents El Paso in Congress.

It doesn't make sense, O'Rourke says, for Salvadorans, Hondurans and Mexicans fleeing violence to get turned away from the United States while Cubans are welcomed without question.

"I want to make sure that this country treats all people who come to our shores and come to our borders with dignity and respect and helps those who are in the greatest need," he says. "We shouldn't, for political purposes, help one group of people over another."

"We have a significant migratory crisis that's building," the Florida Republican said of the "historic increase" of Cubans crossing the U.S.-Mexico border.

Rubio, whose parents were Cuban immigrants, said he's proposing a measure that would let Cubans keep some privileges but crack down on abuses of federal benefits by ending "the automatic assumption in U.S. law that all Cuban immigrants are refugees."

"You'll be legal in this country," Rubio said, "but you're going to have to prove that you are actually coming because you fear persecution before you automatically qualify for refugee benefits."

Cuban officials also criticize U.S. policies, saying they encourage Cubans to risk their lives on harrowing journeys and expose them to criminal exploitation.

Obama administration officials have repeatedly said they have no plans to push for policy changes toward Cubans who arrive on U.S. soil.

No matter what lawmakers decide, many of the Cubans arriving in El Paso this month say it won't make a difference.

"The policy could change," says Cleyzak Muñoz, 34, a merchant from Havana who just arrived. "But what is not going to change is the immigration, because I don't think that Cuba will ever change."

Julio Rojas Rubio, a 33-year-old computer engineer who arrived in El Paso earlier this month, says politicians weighing whether to change U.S. policies toward Cuba should go live there for a few months.

"They would see that most people are leaving Cuba because of a problem with the regime," he says. "Economically, I wasn't doing badly in Cuba. I took care of my family. I lived well. But the regime didn't let me live. ... They repress you. Everything is controlled."

Julio Rojas Rubio was a computer engineer in Cuba; he's been volunteering as a cook at a shelter since arriving in El Paso.

Two journeys, one destination

By day, Lorenzo cut hair at his shop, Barberia El Estilo, in the central Cuban city of Camaguey.

But outside work, he says, he participated in groups that opposed Castro and brought food to jailed political prisoners.

Authorities, he says, threatened him and detained him for days at a time.

Lorenzo says political persecution, not economic necessity, forced him to flee to Ecuador, then head to the United States.

"In this country," he says, "there is freedom of expression."

As Lorenzo describes his run-ins with Cuban authorities, Alexi Fernandez del Risco nods in agreement.

The 35-year-old welder also hails from Camaguey, where Lorenzo started cutting his hair when he was just a toddler.

Things got so bad, Fernandez says, that he tried to leave the island 11 times by boat.

Once, he made it as far as Grand Cayman before he got sent back.

Lorenzo and Fernandez left Cuba and headed to Ecuador separately. The old friends ran into each other by chance this year in Panama, long after Lorenzo last gave Fernandez a haircut.

"I arrived dying of hunger and I saw him and I couldn't believe my eyes. We hugged there in the street," Fernandez says.

Together, they made it onto the last plane out of Panama.

"We arrived together and we're going to stay together," Fernandez says.

But now that they've made it to the United States, they've been sparring over where to go next.

Lessons learned

Norberto Lázaro leans on the cafeteria table and rubs his forehead.

It's only been an hour since he arrived in the United States. He was on the plane that landed in Ciudad Juarez this morning. But it took all day to make it through the U.S. checkpoint. By the time he met volunteers standing outside the Customs and Border Protection facility, the sky was already dark.

"I feel like I'm dreaming," he says.

Rick Vielma interrupts the reverie, asking him whether he has a plan now that he's made it to the United States.

Lázaro says he's ready to start working.

"I want to go up," he says. "I want to go to Alaska."

Vielma tells him he might want to wait before making such a long journey.

"A lot of people when they get here, they're very cold, because of the air conditioning," he says. "It's even colder there."

Vielma speaks Spanish with a Mexican accent. Lázaro asks him if he's from the United States.

"I'm a first-generation American, the first in our family born in the United States. My father is from Aguascalientes and my mother is from Ciudad Juarez. I can't imagine everything you've gone through," he says. "That's why I'm here. ... My sympathy and my heart are with you."

For weeks, Vielma and his 10-year-old son have been stopping by the center to serve food, answer phones and help Cubans figure out their next steps.

Vielma says some of his acquaintances have criticized their efforts.

"They say, 'Why the f--- are you helping the Cubans? You've got family in Juarez.' But people are desperately in need of sleep, of showers, of someone to talk to," Vielma says. "You can't just turn away from this kind of thing."

It's a lesson he hopes his son will never forget.

"I want him to see that it's OK to give," Vielma says, "to see what people are really made of."

'Are you happy?'

The voices of dozens of students repeating their teacher's words bounce off the classroom's concrete floors.

"I am ... you are ... he is ... she is ... we are ... they are ...y'all are."

"You're in Texas," the Rev. Steven Massey tells his class, "so we're going to try to be good Texans."

"Y'all," he says again.

"Y'all," they parrot back.

Just over one-tenth of 1% of El Paso's population is Cuban, according to 2010 Census figures, which show 737 Cubans living in the border city. This month, more than 3,100 Cubans were flown from Panama City to Ciudad Juarez and bused to the U.S. border, Mexican immigration officials said.

Many of the Cubans say they plan to make their way to bigger cities like Miami and Houston. But local officials estimate hundreds may stay in El Paso.

Massey came to El Paso from his home in St. Johns, Michigan, to help start English classes for them.

His immediate goal: teach them a few words and phrases they can use right away as they start to find their footing.

From pronouns and conjugations, Massey moves on to questions.

"Where are you?" Massey tells them. "You say, 'I am in El Paso, Texas.'"

"Why are you here?" he continues. Then he pauses for a moment. "I know it's not a simple answer. You start with saying, 'I am here because ...'"

"Are you happy?" Massey asks over and over, calling on students around the room. All of them say yes.

At the back of the class, Daiye Naranjo Sánchez turns toward her husband and smiles sympathetically.

She can tell he's frustrated. He's looking toward the white board with a blank stare.

"For him, it's like there's a wall inside," Naranjo says. But she's doing everything she can to persuade him not to get discouraged. She hopes he'll become as determined to learn English as she is. It's a tool she knows will help her, no matter what happens next.

"I'm about to face a new life," she explains, "and I don't know what's coming."

Ideal Rodriguez Rivas poses proudly with an American flag someone gave him shortly after he arrived in the United States.

A new beginning

On a breezy spring evening just a day after he first stepped foot in the United States, Lorenzo stands stunned beneath the bright fluorescent lights of an El Paso strip mall.

Heimer brought him to a beauty supply store here to buy him new shears -- ones that will close all the way. He hopes Lorenzo can start working soon as a barber in the United States, and he knows he'll need new tools to do it.

Lorenzo picks out a pair of shears and a package of razor blades, then darts to the back of the store to find a new neck duster.

His eyes well up as he looks at the shelves. He thinks about how much money the new supplies cost, about the pastor's kindness, and about the lies he heard for so many years about evil people in the United States.

"This isn't easy," he says. "In my country, they don't do this."

The store clerk sees him wipe away a tear.

"The difficult part is over," she tells him. "You're here."

Back at the mission, Lorenzo's phone rings.

He laughs as he answers the call from a friend and shouts, "I made it to the United States!"

Now El Paso, he says, is home.