"Make no mistake, it's labor intensive," said Fire Battalion Chief Edgar Davalos, "but the whole thing is we've still got to treat them like human beings, because that's what they are. They're here legally and they're human beings, and we're going to make them as comfortable until they finish their journey as we can."
The deluge of migrants prompted the international humanitarian group Save the Children to come to Deming and set up a "child-friendly space" at the city's migrant shelter. It's the only emergency humanitarian operation Save the Children has ever set up in the U.S. that wasn't in response to a natural disaster.
The group is also working with local law enforcement to spot and support children who've been trafficked or are facing trauma, leveraging their years of experience providing assistance in disaster situations.
"They've been away from their home. They've been in detention. They don't know where they're going," said Jennifer Garner, the actress and Save the Children board member who was touring the shelter on the day NBC News visited.
"They don't speak English. They've been ill. They've gone without baths, without food, without medical care, but they're here, happy to hear me butcher 'Goodnight Moon' because they're children."
The support Save the Children provides is multipronged, but entirely funded by private donation.
Project manager Barbara Ammirati said the organization provides a wide range of resources — including medical supplies, hygiene kits and plush toys — as well as information to help them cope with their changing environments.
"Information so that children aren't frightened," Ammirati said. "They've never been in a bus station before, they've never been in an airport before."
For Betsy, a mother of two from Honduras, the child-friendly space set up by Ammirati's team was a respite for her children, ages 2 and 7.
Betsy said she was fleeing an impossible situation at home. "Lately the narcotraffickers have taken over the country, and they want us to distribute drugs for them. We refused, so they killed my brother," she said. "I'm just asking for an opportunity for my children. I don't want them to be killed."
Betsy and 16 of her immediate family members began the journey from Honduras over two months ago, often struggling to find food and shelter along the way. Only Betsy, her husband and their children made it to the shelter in Deming. Betsy's 12-year-old sister and Betsy's mother, a diabetic, were separated and detained in El Paso after the family crossed the border into the U.S..
On the day NBC News spoke to Betsy, she was booked on an afternoon bus to Miami where her brother, her sponsor in the U.S., would give her a place to stay.
Just hours before her bus was scheduled to leave Deming, Betsy still hadn't been able to contact her mother in the El Paso detention center. Neither of the women had working phones or any way to get in touch.
In March, the number of border crossings by undocumented immigrants, the vast majority of them Central Americans seeking asylum, topped 100,000. Last month, more than 140,000 crossed, overwhelming CBP officers and agents whose job it is to process immigrants and either send them to immigrant detention or release them with a court date, according to government data.