In South and Central America, residents are hearing about migrants stepping off buses into new lives in cities like New York and Washington, DC — but they likely don’t know just how many people are dying to get there.

The Post reported on Tuesday that a 5-year-old girl and 3-year-old boy died while trying to cross the Rio Grande near Eagle Pass, Texas, while an infant was left fighting for life.

And now, sources say that local morgues in that town are running out of space — unable to keep up with the number of migrants who drown while crossing the Rio Grande.

The treacherous trek across the fast-moving river separating Mexico from Texas has claimed more lives in recent weeks than locals know how to handle.

“Every day we get maybe three or four [drownings],” said Tom Schmerber, sheriff of Maverick County, Texas, which includes the 30,000-person ranch town of Eagle Pass.

A recent bout of rain made the already high water levels even more dangerous. Among those who don’t make it are children and pregnant women.

“Last week, one of the morgues didn’t have a place for any more bodies,” said Schmerber. He rejected one morgue director’s request to move bodies to the local jail and “park them outside.” It felt wrong to the sheriff: “I said, ‘No, I don’t want to take the responsibility if an animal comes.’”

A local Maverick County funeral home director told The Post he’s had to “stack” bodies as he runs out of space.

The latest discovery was especially heart-wrenching. “We just picked another baby up — a baby. I’m so pissed I saw a baby,” Schermber said.

The Post was shown tragic photos of migrants found dead over the past few months in Eagle Pass — bodies seemingly bloated and distended from being in the water, faces crusted with blood leaked from the mouth and nose and, perhaps most horrifying, a deceased toddler pulled out of the river.

The boy and his infant brother, from Nicaragua, were being carried across the river by their uncle earlier this week. “As [the uncle] entered the river, it was too deep. The uncle went under. He lost them under the river,” Maverick County Sheriff’s Deputy Santiago “Jimmy” Benavides, 43, told The Post.

The man came up, but the boys didn’t. Their bodies were later pulled from the river.

“I’ve seen hundreds of deceased people who didn’t make it, including [migrants who died from being] dehydrated,” Benavides said. “But when it comes to children, it’s completely different. An adult can make the decision to cross — but not the children. He didn’t get a chance to decide.”

The funeral home director described “decomposed bodies floating on the river,” arriving in numbers he’s never seen in his years working in the funeral home business. “It’s been 16 cases in three days. And it’s not stopping — it’s getting worse. I don’t want this anymore. It’s too sad,” said the 42-year-old, who asked not to be identified.

Since President Biden took office and implicitly promised permanent residence to those who make it into the US, the number of migrant deaths at the southern border has climbed starkly: 300 in 2019; 247 in 2020 — then a record 566 in 2021, followed by 609 this year just through July.

As The Post’s Editorial Board wrote on Tuesday: “That promise underlies every Biden policy on immigration, and it has now engendered a full-blown humanitarian crisis.”

The funeral home director there said he’s been forced to bury anonymous bodies in a county cemetery, after they’re fingerprinted in hopes of eventually identifying them.

A member of the Texas Department of Public Safety (center) holds a migrant child saved from drowning as a group attempted to cross the Rio Grande into the US.

This year he has counted some 300 migrant deaths so far, mainly from drowning or dehydration, and in dire contrast to the pre-Biden border situation.

“The worst used to be 42 cases a year of immigrants,” he said.

Schmerber told The Post his team occasionally discovers bones washed up on the riverbank. “We figure they’ve been there eight months,” he said. “There are probably more dead people around than [have been] found.”

The tragic ways in which migrants perish while striving to make it to the other side is inhumane, the funeral-home director said, adding, “It’s worse than cattle.”

Visitors to Eagle Pass are stunned by what they see — and smell.

“The smell of rot hits you right away — it’s trash, human waste and sometimes decomposing dead bodies,” said John Rourke, an Army vet who runs annual cleanups around the country and spent time in Eagle Pass in August. He regularly posts videos and photos of local tragedies like, this week, the decomposing body of a man crumpled along the side of the road after not surviving a Rio Grande crossing.

“Disgusting, awful, tragic. It’s unbelievable,” he said. “They’re literally starting to just bury people without even knowing who they are or getting ahold of their families.”

The mounds of discarded refuse — dirty diapers, clothes, pills, documents — makes Eagle Pass “more like the landfill of Maverick County,” said Rourke, who founded Blue Line Moving.

Among the trash are bits of carpet.

“[Migrants] tie carpet to the bottom of their shoes so they can’t be tracked when they’re walking through the desert,” said Rourke, who’s returning to the area next month with his cleanup crew.

He was particularly disturbed by the sight of used condoms strewn along the side of the road. “You just crossed the Rio. It’s not like someone says, ‘This feels like the time we should do it, honey,’” said Rourke, citing the rape of women and girls by “coyotes” trafficking migrants across the border.

“These small border towns are overrun, their budgets are completely blown,” said Rourke, who plans to donate money raised for his Great American Cleanup mission to the Eagle Pass sheriff’s office. “This isn’t normal sheriff’s work. It’s not about fighting crime for them. It’s a rescue mission every day for them.”

Meanwhile, Rourke said, “The people of Eagle Pass are absolutely prisoners.” In addition to the trash and deaths, he added, residents have migrants pounding on their doors in the middle of the night, asking for help, and defecating on their lawns.

“No one will buy a house in Eagle Pass,” Rourke said, noting that locals have told them they can’t sell their homes and leave.

Schmerber recalled how, growing up in Eagle Pass, “Everyone knew each other and life was peaceful.”

These days, he said, neighbors feel terrorized.

“People say they’re afraid to go out. People live in fear,” Schmerber said, noting a recent rape of a 73-year-old local woman by a Honduran migrant and regular weapons thefts from ranches in the area.

“I’m going to keep doing my cleanups and showing these videos because it’s not right,” Rourke said. “And it’s not right to the people who came here legally. And for the people who live in that sorry-ass county and can’t get out.”