“We’re a dumping ground – we’re like the garbage can of the world,” he said, a new phrase in his increasingly inflammatory campaign against immigrants.

These pledges were lapped up by the younger crowd, many voting for the first time in a presidential election. One of the biggest cheers came when Trump called for the death penalty for any migrant who kills an American citizen, part of a crackdown on immigrant gangs. “We’ve got to get these animals out of here fast,” he said.

Research shows young men are much more receptive to the message of Republicans, and of Trump, than young women. And Trump has courted them with rhetoric that espouses macho bravado and his closeness to figures popular with young men – billionaire tech bro Elon Musk, Barstool Sports founder Dave Portnoy and UFC president Dana White among them.

Writing in The New York Times this week, John Della Volpe, director of polling at Harvard Kennedy School Institute of Politics, called Trump’s campaign “a masterclass in bro-whispering”. And he noted his research showed Trump had halved the Democrats’ lead among registered male voters under 30 since 2020.

Part of that may also be Trump’s success on social media platforms such as TikTok, on which both candidates’ campaigns have stepped up efforts. Trump has amassed 12.4 million followers on that platform since joining in June.

At Wednesday’s rally, Trump gave a shout-out to Carson Carpenter, president of College Republicans at ASU, a group that calls itself “the fastest growing conservative movement at the largest university in America”. With so many students, naturally some will be conservative, but 20-year-old sports and business junior Logan Eckerfield – a locked-in Trump supporter – says it is still far from the norm.

“On campus we’re definitely the minority,” he told this masthead while waiting for the Republican candidate. ”Most college campuses are blue [Democratic]. But there’s no hate between anyone; there’s no violence at all. Nobody feels that deep about it.“

Eckerfield’s support for Trump was simple. “I want closed borders, I don’t want people coming in. There’s a lot of crime coming into Arizona,” he said. ”The more people that flood in, the more crime that’s gonna come in.“

Typical of the students I spoke to at ASU, Eckerfield was not comfortable with Trump’s behaviour towards women, or his alleged praise for Hitler’s generals, or his denial of the 2020 election result. But also typical was his capacity to overlook those parts of Trump’s character.

“It definitely does [bother me] but with my family and a lot of things, financially, it just makes more sense for Trump to be in office,” Eckerfield said. ”Both sides, they say things I don’t agree with. I just have to go with what I agree with more.“

Sisters Calypsi and Cairo Bailey had a similar take. “He has said some stupid stuff, but I’m not voting for the perfect person, I’m voting for his policies,” Cairo said.

Calypsi had a strong disdain for identity politics, something she felt motivated many of her friends. “A lot of my friends that support Kamala, they really only want a woman in office that’s black, and I feel like that’s a dumb reason to vote for someone,” she said.

”Life was so much better when he [Trump] was president. Dude, gas prices were cheaper – literally everything was cheaper – and I felt so much safer.“

Later, Trump travelled to Las Vegas in Nevada, the other crucial swing state in the country’s west, where he spoke at a rally hosted by the Turning Point political action network, co-founded by 31-year-old conservative activist Charlie Kirk.

“He likes young people,” Trump said of Kirk. “People have no idea how many young people there are that are conservatives in this country.”

Turning Point is one of the groups to which Trump has outsourced much of the groundwork of the campaign, rather than the Republican Party’s apparatus. It targets students and evangelicals, but there is scepticism about how much money it can really raise, and how many voters it can turn out.

Among the neon lights and slot machines of Sin City, a looser, more energetic Trump emphasised his election commitment of “no tax on tips”, as well as no taxes on overtime payments or social security benefits for seniors. “All three are very good for this room,” he said.

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A confident Trump also claimed, wrongly, that he was ahead in key swing states such as Nevada, Arizona, Michigan, Pennsylvania and Wisconsin. “I’m not supposed to say it, but we are leading by so much,” he said. Most polls show the race is too close to call in those key states.

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