McALLEN, Texas—They come in pairs, worn-out migrants carrying—or, in some cases being led by—children who range in age from infants to teenagers. Many of the adults weep openly when the doors to the parish hall of the Sacred Heart Catholic Church in McAllen swing open and nuns, Jesuit priests and a host of local volunteers rise to their feet in a raucous standing ovation.

"Bienvenidos!" shouts volunteer Hermi Forshage, clapping. "Bienvenidos! Welcome!"

The migrants are too tired and disoriented to notice Forshage; they're eager for an opportunity to wash, eat, and rest. Each is an undocumented family from Central America—Honduras, El Salvador, and Guatemala, mostly—that is helping fuel what U.S. President Barack Obama has called a "humanitarian crisis" along the U.S.-Mexico border.

Most of the children who passed through the church one day last week were young, part of the recent surge in children under 12 caught at the border. There has been a 117 percent increase in the number of unaccompanied children caught at the border this year, compared with last year, according to the Pew Research Center. The number of children accompanied by an adult, meanwhile, has tripled, to more than 20,000.

Thousands of unaccompanied minors are housed in detention centers, but the families coming to the Sacred Heart Church represent that latter group—they are among the more than 55,000 migrants who have been provisionally cleared by U.S. Customs and Border Protection since the beginning of the year. They've been given temporary papers and can live with family members while awaiting a court date.

Sacred Heart sits in the center of McAllen, which has become ground zero for the immigration debate. The city is just five miles north of the U.S.-Mexico border, and Spanish is the lingua franca here. U.S. Customs and Border Protection has a detention center in town and opened another in nearby Harlingen.

View Images Ana Garcia, 36, and her son, Josè, 13, from Guatemala rest at Sacred Heart after showering and eating. Photograph by Jennifer Whitney, The New York Times/ Redux

Previous waves of migrants were sent to other states, including California, where they were met with hostility and demonstrations. The reception in some other places, from Maine to Virginia, has also been frosty, helping fan the flames of the immigration debate in Washington.

House Republicans passed a bill before leaving for summer recess that would allocate $694 million to address the border crisis, far short of the $3.7 billion had Obama requested, but enough to appease the right wing of the party. Obama lashed out at Republican leaders, calling the bill "extreme and unworkable." There are reports that the president may be preparing use his executive power to put off deportation for millions.

The migrants passing through Sacred Heart will tell you that those fleeing violence and chaos in Central America aren't likely to stop unless their home countries offer their citizens reasonable levels of safety and opportunity.

For many, the first glimmer of those ideals in the United States come at Sacred Heart Church.

The program here is run by Catholic Charities USA. Sister Norma Pimentel, executive director of Catholic Charities for the Rio Grande Valley, began routing families to Sacred Heart last June, when she learned that Border Patrol officers were dropping them off at a nearby bus station.

Since then, about 5,400 migrants have passed through the church on their way to all four corners of the United States. Some will keep their appointments with the American judicial system and apply for asylum in the weeks to come. The success of their petitions to stay will depend on many things, including how threatened they were, whether they were directly affected by violence, and how much of their decision to leave was based on choice.

Many will decide to skip the legalities and simply slip into the mass of undocumented migrants.

View Images Piles of donated water and other survival necessities are stored at Sacred Heart's emergency shelter. Volunteers give the migrants supplies as they head out to their next destinations. Photograph by Jennifer Whitney, The New York Times/ Redux

"Don't Worry, You're Here Now"

For Sacred Heart's nuns and volunteers, the church is a refuge from the politics and rage of the national immigration debate.

"We always say, leave politics at the door," says Brenda Rioja, the editor of a local church newspaper and the mission's spokesperson. "It's about helping those who are right there in front of you. Imagine if we did that all around the world, how different it would be."

Jose Matias Garcia, a 33-year-old shop owner from El Salvador, walked through Sacred Heart's doors with his 11-year-old daughter Daniella one recent early afternoon. Garcia hated to break up his family but says he had to when ongoing extortion by the local MS13 (Mara Salvatrucha) gang got too expensive.

Since April, he had been paying them $50 a week. Then gang members increased their take to $100. Extortions of small businesses and families have become commonplace, even routine, in many parts of El Salvador and Honduras.

For Garcia, the message was clear: Pay up or be killed. He sent his wife and two older children to live with his parents in another town with fewer problems.

Jose and Daniella fled north. They hired a Mexican human smuggler, known as a "coyote," and traveled by bus to Reynosa, along the border. Garcia said he paid about $500 to Mexican police and army officials along the way, but made it.

"Don't worry, you're here now," Forshage tells them.

She votes reliably Republican and is "not a fan" of President Obama but insists that the migrants who have already arrived, like the Garcias, deserve a chance to make it work here. This half of a broken family is headed to Georgia, where they'll be met by Garcia's mother-in-law, who arrived seven years ago and obtained her green card.

"I can't imagine having to sell everything and leave my country with just my children," says Forshage, who has come to the center every day since June 12. "You know you're doing the right thing here."

Forshage lives on a ranch north of McAllen, where she and her husband receive regular visits from migrants passing through their land asking for food, water, a ride to Houston. She helps with food and water but usually calls the Border Patrol to come and pick the travelers up.

At Sacred Heart, she talks the migrants through the next steps in their journeys: From the church they'll board buses that will take them north to Houston. They'll pass through another Border Patrol checkpoint, but now they're carrying papers given to them by U.S. Immigration and Customs Enforcement (ICE).

One Honduran mother-son pair was headed to North Carolina. A Honduran family was bound for Chicago. A young man from El Salvador wanted to reach Los Angeles before August 2, so he could celebrate his 30th birthday with his son.

View Images Yorfrin Daniel Cruz, 7, arrived from Honduras with his mother and brother, who are also staying at the shelter. Photograph by Jennifer Whitney, The New York Times/ Redux

New Country, New Challenges

Most of those passing through the church don't speak English. A few Guatemalans have come through who don't even speak Spanish, but rather one of several indigenous languages related to ancient Mayan. Forshage makes sure to tell the migrants that the journey isn't over yet: "There are good people and bad people out there."

Nearby, a Guatemalan woman named Dilma and her 7-year-old daughter Lucky had just showered and eaten. The next day they'd board a bus for Oakland, California, where Dilma's brother lives.

When the crisis began, the church fed migrants heaping plates of chicken, rice, and beans.

But many were so starved that they couldn't stomach the hearty portions, so the staff switched to lighter fare, like brothy soups. Everyone is allowed to shower, sleep on cots erected in the parking lot, and browse through used clothes donated by a local shelter.

Volunteers scurry around helping the migrants find clothes, shoes, hair pins, stuffed animals, plastic jugs, backpacks—anything that will make the trip a little bit easier.

Elsewhere in the room, lawyers for a local civil rights organization strategize about what legal aid to offer the recent arrivals. They schedule talks with some migrants and dish out ad hoc advice to others.

"They come in here dirty, exhausted, hungry, they look gray," says Forshage, "but a three-minute shower, a little food, a quick nap, and they're like different people."

She squeals at the sight of 11-year-old Daniella Garcia. "Look at you, beautiful," she says in Spanish. "Are you feeling better?"

The little girl nods shyly, wraps a finger around a long, dark braid. She says she's looking forward to learning English, going to school. She misses her friends back in San Salvador already, she says, and of course her family.

Forshage tells Jose that Georgia is four bus rides and several days of travel away. He hopes to bring his family there someday, he says.

"And hopefully you will," says Forshage. "This is the first step."

She hands him the envelope with his court date, bus tickets, and a map of the United States.