EXCLUSIVE: McALLEN, Texas — Life jackets of all sizes and the occasional punctured raft are strewn along the banks of the Rio Grande, just south of Mission, Texas, where a relentless onslaught of illegal immigrants eagerly surrender to beleaguered Border Patrol agents around the clock.

It’s a cycle for which there is no end in sight.

“You're going to be out here a long time,” Fernando, an El Salvadoran child, told FoxNews.com shortly after surrendering to Border Patrol authorities after midnight Saturday. “There are thousands of us."

With most of the men and women charged with securing the Mexican border busy processing some of the 60,000 illegal immigrants who have made the harrowing - and sometimes deadly -journey to the American border in the past nine months, only a handful of Border Patrol agents drive the riverside loop in a small town called Granjeno just south of Mission, in the Rincon peninsula.

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Illegal immigrants of all ages, including many unaccompanied children, run to them to surrender. They are piled into the back of Border Patrol vehicles and taken to a makeshift staging area in Rincon Village, where a large Border Patrol bus waits to transport them to McAllen’s Border Patrol facility.

FoxNews.com accompanied Texas lawmaker Louie Gohmert, a former judge and current Republican Congressman, to the site in the pre-dawn hours of Saturday. Gohmert, whose district lies some 550 miles northeast of what has become the most heavily-trafficked people-smuggling route in the world, has been to the location many times, but has never seen it so understaffed and overwhelmed.

“I’m more concerned than ever [that the border is] so seriously undermanned and I’ll be raising hell in Washington,” Gohmert, who invited FoxNews.com to see the situation first-hand, would later tell Border Patrol officials.

The Border Patrol agents loaded and unloaded their vehicles packed with the newly-arrived illegal immigrants — including women pregnant or nursing infants, and small, unaccompanied children — throughout the evening and early morning hours. At first, they were mostly teenagers, ages 14 to 17, arriving with their mother or brothers or no one at all. Then came the pregnant women. A mother nursing her infant. A small girl with wide eyes clutching a doll.

A total of 72 came in during the first dark hours of Saturday morning. A third were unaccompanied children.

The life jackets helped many make it across the Rio Grande from Reynosa, the Mexican city across the water from Mission, just west of McAllen. Sources say they come over on rafts ferried by the so-called “coyotes,” the human smugglers whose means of transport are rendered useless whenever discovered by the Border Patrol. Many don’t make it across the river; multiple sources became emotional when recounting their discoveries of small, lifeless bodies washed up along the riverbank.

Tens of thousands of illegal immigrants have flocked to the U.S. in recent months, believing the Dream Act, as well as a 2008 law that grants an asylum hearing to any child not from a border nation, and the White House policy known as “prosecutorial discretion” means once they arrive, they’ll never have to go back.

The Obama administration has said many will be returned to their homelands, but thousands have been dispersed around the country, sent to military bases or one of the nearly 100 Health and Human Services shelters run by private contractors or faith-based organizations. From there, they are typically turned over to a parent or relative already in the U.S. or released to a sponsor organization and given a court date for their hearing.

Many of the illegal immigrants tell Border Patrol and Texas state authorities they learned from the media in their home countries that if they crossed the border to the U.S. right now, they’d be given papers and allowed to stay, border sources who interview the immigrants told FoxNews.com.

The number of illegal immigrants apprehended at the border in the past nine months is more than double last year’s total. Most come from Honduras, El Salvador and Guatemala, traveling up through Mexico to the border aboard an infamous train known as “The Beast.” From there, coyotes help them traverse the hardscrabble Rio Grande valley, and the serpentine river that winds through it. In May 5,366 illegal immigrants were detained in the Rio Grande Valley Sector. Last month, that number skyrocketed to 30,380, according to a law enforcement document obtained by FoxNews.com.

FoxNews.com witnessed the seemingly endless parade of illegal immigrants as they turned themselves in to agents and climbed into the vans. One mother teared up when telling FoxNews.com of her family’s perilous journey from Honduras. Some said the trip took as little as two days, others said they'd been traveling for months. In groups of 12 or more, they were then taken to the bus set up in a desolate area at the intersection of unlit dirt roads in Rincon Village along the river for initial processing under the full Texas summer moon.

“They just keep on coming,” one Border Patrol source said.

The same source noted that last week’s derailment of “The Beast” had temporarily stemmed the tide. Now that it’s up and running again, U.S. authorities here at the border are racing for even higher numbers.

Agents normally accustomed to working in the field waited at the bus, donning blue latex gloves as they examined the incoming illegal immigrants. They asked questions, searched belongings for contraband and tried to determine if the immigrants need medical help.

Most of the illegal immigrants appeared to be in clean clothes and good health — the biggest complaint FoxNews.com heard was from a child who had lost a shoe in transit. All looked very happy to have finally arrived on U.S. soil.

But appearances are deceiving, one border source said.

“Many of them have scabies, lice and sometimes serious infectious diseases that have not manifested themselves yet,” the source said.

From the staging area, the illegal immigrants were taken to the McAllen Border Patrol headquarters a short ride away. Though it is technically a processing center, the sheer size of the current influx has rendered it something more akin to a detention facility. By Saturday morning, it held 480 immigrants, about 100 more than their capacity. A few weeks ago, it held 1,200, Gohmert and Border Patrol sources told FoxNews.com.

A warehouse nearby with a 1,100 planned capacity was supposed to open its doors July 11, but a botched contract for air conditioners postponed the opening, according to a request for bids posted on the federal contracting website.

With the facility crammed beyond its capacity, the undocumented immigrants are being bused and flown to several other processing facilities along the 2,000-mile border, in El Paso and in California, where angry residents of Murrieta, a small city just north of San Diego, have turned away hundreds of illegal immigrants brought by the federal government for processing.

The veteran Border Patrol agents know that with their attention diverted to women and children, the border at times in locations such as along the Rincon Peninsula appeared virtually unprotected from dangerous drug and weapons traffickers with motives far less innocent than finding a better life. During the first 90 minutes FoxNews.com spent with Gohmert, no Border Patrol agent, Texas Department of Public Safety officer or any other member of law enforcement was visible.

We weren’t the only ones watching for them: a lookout perched atop a tall structure resembling a water tower located near the road quickly jumped off and ran toward the river after spotting our car coming down the dirt path. Border sources noted illegal immigrants typically run to cars to surrender; only those involved with cartels or gangs are likely to flee.

The cartels or coyotes or other criminal organizations have networks of people — often juveniles — paid to stand watch from points of high elevation on both sides of the border.

Early Saturday, whistles and signal calls echoed in the night air from across the river and in our midst, the clandestine communication of coyotes and cartel members using the border crisis to profit. As we moved, on foot or by car, through the thick brush toward the river or down the rocky path, we heard them all around us, moving with us, at some points frighteningly nearby.

When a Border Patrol official finally approached our group, he told Gohmert there were only three Border Patrol agents assigned to this large swath of border. They know it is a busy route, but they were so busy with processing the steady flow of children and families that the area appeared largely unpatrolled.

A recent law enforcement bulletin put the crisis in the Rio Grande Valley sector in the flat language of bureaucrats.

“Total apprehensions in the RGV Sector are at historically elevated levels, and include greater numbers of other-than-Mexicans and unaccompanied alien children than any other sector along the U.S. –Mexico border,” read the bulletin obtained by FoxNews.com. “Total apprehensions are now highest in the RGV Sector, which represents a noteworthy change from previous years.”

On the ground, border agents explain the situation in more conversational terms.

“There’s been a dramatic, serious uptick beginning in January,” one border source told FoxNews.com. "We've never seen this before — unaccompanied alien children and big groups of families.”

And in a twist, the cat-and-mouse game Border Patrol agents have played with illegal immigrants for decades has changed as their quarry no longer hides.

“We used to chase after them; now they are chasing us,” one official said.

Israel Cardoza and Kaye Cruz contributed to this report