While Boston’s Cardinal Sean O’Malley distributed Communion through the slats in the tall fence at the Mexican border to believers on the other side, hands reached out through the bars.

“We have lost a sense of responsibility to our brothers and sisters,’’ O’Malley said in his homily at the Mass in the Desert, quoting Pope Francis in a sermon that highlighted the 400 bodies found near the border every year and the 25,000 children, most of them Central American, who arrived in the United States last year unaccompanied by an adult.

In an interview during two days of events surrounding a push for immigration reform, I asked O’Malley about a bishop’s remark to me earlier in the day that comprehensive reform was a “dead dog, and the only question is whose porch it winds up on.”

O’Malley laughed and said, “That’s an interesting metaphor” on “an issue on which we’ve had many false starts.” But the way our government treats migrants, he said, is not something he and the seven other American bishops who came here can ignore, or that the church as a whole can, either.

“These immigrants are not different from our parents, grandparents and great-grandparents who left horrific situations because they had the courage, the ambition, the desire to do something for their children,” he said.

During the 20 years he worked in Washington in the 1970s and ’80s, O’Malley said, “most of my parishioners were undocumented refugees. To me, they’re not statistics; they’re people, and I’ve seen the kinds of sacrifices and the suffering they’ve endured.’’

The inspiration for this trip, he said, “was Pope Francis’s very first journey’’ after becoming pontiff, to the Mediterranean island of Lampedusa, “where thousands of people have perished trying to get into Europe, and we have a very similar situation here.” Francis visited Lampedusa to remember the 366 migrants who died when a boat sank off its coast last October.

On Monday, several bishops met with the weeping mother of a 16-year-old boy shot to death by U.S. Border Patrol agents two years ago. Authorities said the shooting occurred after someone threw rocks at the guards, but news reports said it wasn’t clear that the boy, Jose Antonio Elena, was involved. The boy’s family said he had just gotten off work at a nearby convenience store and was on his way home when he was shot 10 times.

The bishops also crossed the border on foot and met with women staying in a shelter run by nuns in a high-rise apartment building ringed with plastic bags, bottles and other trash. Three of the women said they’d been fleeing domestic abuse when they were deported, although the shelter isn’t specifically for abused women. A fourth said she’d been deported after she got sick in a detention center in Eloy, Ariz., where she was held for six months after being picked up by police at the border. The facility, privately run by the Corrections Corp. of America, needs to keep its beds filled to maximize profits, she observed. (According to the Immigration Detention Justice Center, Eloy is “under close watch by human rights groups due to the high number of inmate fatalities.”)

In their black clerical garb and pectoral crosses, the bishops also served dinner to deported migrants at a soup kitchen run by the Kino Border Initiative, named for Eusebio Kino, a 17th-century Jesuit priest. The soup kitchen, funded in part by a grant from the U.S. Conference of Catholic Bishops, is not far from where the 1963 Sidney Poitier movie “Lilies of the Field” was shot, said a priest who works there.

The small serving space has canvas walls, a tin roof and a concrete floor. Up in the hills just across the road, adolescent lookouts with walkie-talkies let gang members know when deported migrants are coming across the border, and many of the migrants are robbed or rounded up by ‘coyotes’ promising to get them back into the United States for an exorbitant fee. “If there were a viable legal way to get in, they would take it,’’ said the Rev. Sean Carroll, a Jesuit priest who has been working here for the past five years.

At the long metal tables of the soup kitchen, retired bishop Ricardo Ramirez of Las Cruces, N.M., spoke in Spanish to three men who had been deported. “You have the features of a Mayan god,’’ he told Tomas Dominguez Avila, 24, who is originally from Guatemala. Avila came north on a 15-day train trip that he spent hiding in a space just above the train’s wheels, tied into place to keep from falling onto the tracks. He was arrested, he said, after authorities in Danville, Ky., where he’d been working in a Chinese restaurant, asked to see his Social Security card.

Like many of those here, his plan is to find a “good sponsor” — a coyote he’d pay to smuggle him into the United States. He said he knows that some “sponsors” rob and even kill their customers in addition to overcharging them, “but there are good smugglers and bad smugglers.”

Every day in the United States, about 1,000 deportations are reported, many of them tearing apart families. Gustavo Sanchez, 24, is desperate to get back to the wife and two children he was supporting with construction work in Phoenix until, he says, he was stopped while riding a bike with no light on it at night.

The Catholic leaders who’ve come here to advocate for change only have to convince a couple of key players: President Obama could curtail deportations without congressional approval. And House Speaker John A. Boehner (R-Ohio), himself a Catholic, would simply have to allow a vote on comprehensive immigration reform, although he isn’t expected to do so until after the midterm elections this fall .

“I’m told we have the votes, so we have hopes,’’ said O’Malley, who didn’t mention either Boehner or Obama by name. “But we’ve had hopes before.”