Few of the men at a Tijuana migrant shelter fit the profile of ‘bad hombres’ and existing measures are keeping them out

When Donald Trump views the prototypes of his proposed border wall outside San Diego on Tuesday he could say, truthfully, that just a few miles south there are hundreds of Mexican men desperate to break into the United States.

You can find them at shelters like Casa del Migrante, a hostel for migrants in Tijuana, a sprawling city with a soaring murder rate. They admit they have no permission to live in the US and are determined to enter illegally.

Some have glimpsed the prototypes the president will inspect and concede they look formidable: 30ft high with state-of-the-art technology to withstand or impede blowtorches, jackhammers, ropes and ladders.

“Honestly, I don’t know how I’d get over it,” said Félix Mateos, who saw the eight prototypes last week while trying to sneak across the border.

The stories of Mateos and many other would-be border crossers here, however, dent the case for the wall.

Few seem to match the “bad hombres” – rapists, murderers, drug traffickers – that Trump conjured to sell the wall to voters during the 2016 election.

An increasing proportion are people who lived for years or decades in the US, working and raising families, and were deported for minor infractions.

Mateos, 54, lived in California since the age of 16 and harvested grapes, nuts and peaches in the fields around Modesto, earning $14 an hour.

Facebook Twitter Pinterest Félix Mateos, a farm worker deported from California, at a migrant shelter in Tijuana, Mexico. Photograph: Rory Carroll/The Guardian

Last October, police stopped him for driving without a license and he ended up in the hands of Immigration and Customs Enforcement (Ice), one of an increasing number of undocumented migrants swept up for minor offences.

Mateos paid a lawyer $7,000 – almost his entire savings – but an immigration judge ruled against him, unmoved by the fact the labourer had three children, aged two, eight and 11, who were US citizens.

Deported to Tijuana just before Christmas, Mateos resolved to find a way back – to make the “brinca”, the jump.

“I miss my children,” he said, his eyes watering. His partner works part time washing dishes in a restaurant, not enough to support the family. “I need to work. What will become of them?”

Deportees with deep roots in the US account for an increasing number of the shelter’s population, which totalled 7,000 last year, said Valeria Griego, a Casa del Migrante administrator. They are highly motivated to return – about 70% try at least once, she said.

Salomón Cortés, 28, was one of them. He used to run the kitchen in an Italian restaurant in New Jersey – his speciality was pasta Alfredo – and had a four-year-old son there, William. The name is tattooed on his arm. “A father should be with his son,” he said.

Facebook Twitter Pinterest Salomón Cortés, who has been caught 14 times trying to enter the US, at a migrant shelter in Tijuana, Mexico. Photograph: Rory Carroll/The Guardian

Bad hombres or not, there is another reason these would-be border crossers dent the case for the wall: they can’t get in.

They have tried and failed – stymied by the existing barriers and surveillance networks operated by the border patrol.

Cortés, who returned to Mexico to marry, said he has tried 14 times to re-enter the US – detected each time by border controls that have been steadily expanded and militarised by successive presidents since Bill Clinton.

For his last three effort,s Cortés spent three months in detention in Texas, six months in New Mexico and six months in California.

If caught again he faces two years in detention. “It’s ugly in there, it’s hard. I don’t want to risk it,” he said. Cortés said he has now decided to stay in Mexico.

Border crossings are near historic lows and in recent years it is estimated that more Mexicans are voluntarily leaving the US than entering – a product of economic and demographic shifts. Still, Trump has made the wall a keystone of his immigration crackdown.

Mateos, the farm labourer, last week tried to sneak in with two friends via Otay Mesa, near the wall prototypes. Two border agents on motorcycles caught them within three minutes.

Mateos was deported the next day to Tijuana.

Though limping from a fall while scaling a 6ft barrier, he intends to try again. “At least once, maybe twice.” He cannot afford the $8,000 to $15,000 charged by coyotes – the nickname for people smugglers – so will make another amateur effort. If he fails – a fate suggested by his tears and defeated demeanour – he said he may bring his children to Mexico.

Mateos did not have an opinion about whether it made sense to build a 30ft wall along the border. “That’s for Mr Trump to decide. All I know is the prototypes are very tall.”