EL PASO, Texas — It’s been known as “Nicholson’s Crossing” since anyone can remember — the spot under a downtown highway overpass where Jack Nicholson filmed “The Border.”

The actor played Charlie Smith, a corrupt border guard who accepted payoffs from Mexican traffickers making their way into this dusty city in west Texas in the 1982 film.

Now, nearly 40 years later, “Nicholson’s Crossing” has become “ground zero” for the thousands of migrants who every week cross the Rio Grande — in this area, a dried-up river bed strewn with stray plastic bags and scrub.

The migrants, most of them from Central America, give themselves up to green-uniformed US Customs and Border Protection agents who wait in their white and green SUVs under the dusty overpass.

On Monday, The Post went on a ride-along with CBP agents, and witnessed them apprehending nearly two dozen migrants who crossed the river and made their way to the highway overpass under a blistering afternoon sun.

“I’ve never seen numbers like these in the El Paso sector before,” said David Zapp, a 20-year CBP veteran, who started his career patrolling the Canadian border at Niagara Falls. “There are some days we have a constant flow across the border.”

El Paso, a city of nearly 700,000, has lately been overwhelmed with the flow of migrants. US Border Protection officials told The Post that they apprehend more than 800 migrants a day. One day last week, they took in 1,700 people.

The agency is so overwhelmed by the influx of illegal immigrants that they recently began construction on a tent facility on the outskirts of the city, in the foothills of the towering Franklin Mountains. The tents can shelter up to 500 people at a time.

“These temporary facilities will support our efforts to process, care for and transfer the unprecedented number of families and unaccompanied children crossing the border each day,” said John Sanders, CBP’s acting commissioner.

Last month, CBP came in for sharp criticism from local politicians and advocates when it began to house dozens of illegal immigrants in an impromptu shelter under the Bridge of the Americas, which connects El Paso to Ciudad Juarez, across the border.

Local charities who take asylum seekers after they are processed by federal authorities have been housing them in hotels around the city. Last week, Annunciation House leased an abandoned warehouse in the eastern part of the city to temporarily house more than 1,000.

On Monday, The Post saw a bedraggled group of 16 adults and three small children — from Cuba, El Salvador, Guatemala and Honduras — calmly walk up to a border patrol agent, some carrying their meager belongings in a plastic bag.

“The majority of the people we catch just walk up to us,” Zapp said. “They are not trying to evade arrest. They want us to take them in.”

Indeed the scene Monday had a surreal vibe to it as a couple that looked dressed more for a day of sightseeing than a border crossing — he in sneakers, sweatpants and
a long-sleeve T-shirt and she in a Pink-brand tee with gray leggings and matching lightweight hoodie — walked up to CBP agent Edward Butron.

Yudier Angel Guerrero, a 29-year-old fisherman from Holguin, in eastern Cuba, and girlfriend Lina Telles, 20, calmly held out their right arms as Butron placed bright-orange wristbands on them as if they were headed into a nightclub.

Guerrero said he was relieved to see border agents after his long journey from the Communist island.

“We were so happy to see the patrols,” Guerrero said after he got his identification bracelet.

He told The Post that he and another group of 10 Cuban asylum seekers left their country in February, traveling north through Panama, Central America and Mexico. It was his second attempt to cross into the US, he said. A few years ago, he attempted to cross on a raft to Florida.

“We want to stay here, because this is the country of freedom,” he said in Spanish.

Darwin Hernandez, from El Salvador, began to tear up as he stood under the bridge waiting to be processed by the agents. He described his month-long journey through Guatemala and Mexico carrying his 9-year-old son Jose Arnalfo, who suffers from cerebral palsy.

“It’s too dangerous to live in El Salvador,” said Hernandez, who works as a clerk in a municipal office near San Salvador. “Gangs extort everyone, and threaten to kill you if you can’t pay.”

Since last summer, when people began to come en masse, Zapp, 42, heard similar stories over and over again. He is one of 2,000 federal border agents covering west Texas and all of neighboring New Mexico — an area encompassing 125,688 square miles. Agents typically patrol the area over 10 hour shifts.

In relentless heat, they ride on dirt roads through desert and scrub next to an 18-foot border fence that was constructed during the last Bush administration.

In nearby Sunland Park, New Mexico, the fence overlooks a shantytown of half-finished brick homes with cardboard for windows on the other side of the border. Residents of the Rancho Anapra neighborhood frequently throw rocks across the border fence, targeting Border Protection agents.

Given the recent influx of migrants, Zapp said he’d like to see a consequent increase in border agents.

“All of our federal agencies are working really well with Mexican and local authorities, but the flow continues and it’s probably going to spike,” said Zapp. “We need more agents.”

One CBP agent recently patrolled the area in an SUV covered with fencing — a prototype designed by the agents themselves to protect them from the frequent “rockings.”

Before the fence was built thieves from the Mexican side of the border would attack Union Pacific trains that pass through the area, robbing them of merchandise as they passed through the isolated desert terrain.

“They would hijack trains, cut the cargo boxes and steal whatever they could, “ said a Border Protection agent.

In 2002, when there was just a flimsy chain-link fence dividing the border, drug traffickers kidnapped a group of FBI agents and took them to the Mexican side where they were assaulted and tortured.

They were rescued by a group of Border Protection agents.

Asked if they support a reinforced border fence, most of the CBP agents interviewed by The Post echoed Zapp’s thoughts on the matter.

“It’s not going to stop illegal entry,” he said, “but it will give us agents more time to be able to respond to a situation more effectively.”