PRESCOTT VALLEY, Ariz. — Former president Donald Trump, during a campaign rally Sunday in Arizona, proposed a dramatic expansion of the Border Patrol, looking to deepen his commitment to border security — an issue where his Democratic opponent, Vice President Kamala Harris, has sought to challenge him.

Addressing an enthusiastic crowd in this border state, Trump promised he would set a goal of hiring 10,000 Border Patrol agents and “immediately” ask Congress to give all agents a 10 percent pay raise. He also pitched a $10,000 “retention and signing bonus” for agents.

“It’s almost like being a great baseball player or football player, but not quite as much money, but not bad, right?” Trump said, surrounded onstage by Border Patrol agents. “We’re going to retain them, and they deserve it. They’ve been treated unbelievably badly.”

Trump did not offer further details, but his pitch is an ambitious and potentially difficult one for an agency that is already struggling to grow its ranks. There are fewer than 20,000 agents with the Border Patrol, responsible for apprehending migrants illegally crossing the border between ports of entry, so Trump’s proposal would mean a 50 percent increase in the agency’s size.

The Harris campaign dismissed the proposals that Trump made Sunday as “phony,” noting that he has previously made promises about border security — like having Mexico pay for a border wall — that have not come to fruition.

“Trump doesn’t care about solving problems, he only wants to run on one,” Harris campaign spokesperson Matt Corridoni said in a statement. “That’s why he killed the bipartisan border bill that would’ve secured the border, despite the fact that it was endorsed by the Border Patrol.”

Harris has been campaigning heavily on her embrace of a bipartisan Senate border deal that Trump helped defeat this year, one that would have added more than 1,500 personnel to Customs and Border Protection, including Border Patrol agents. Trump rallied congressional Republicans against the proposal, giving Democrats an election-year opening on an issue that has historically favored the GOP.

Adam Isacson, a border security analyst at the Washington Office on Latin America, said Trump would be taking on a long-running staffing problem at Border Patrol that stems from a range of factors. One of them, Isacson said, is the extensive background screening for prospective agents, which includes a polygraph test that most candidates fail.

“This has been a chronic problems for many years,” Isacson said of Border Patrol staffing. “Trump would have to really lower hiring standards to get there.”

Isacson also said CBP’s staffing needs are most pressing at ports of entry, which are staffed by CBP officers, not Border Patrol agents. The agency says more than 90 percent of the fentanyl that it intercepts is at ports of entry, where cartels try to sneak it in using vehicles.

Trump has long championed cracking down on illegal immigration, and he is spending the final weeks of the campaign leaning into an especially nativist message. He visited Aurora, Colo., on Friday — the site of false claims he has made about the presence of Venezuelan gang members — and proposed a deportation program under a law that was last invoked during World War II to intern immigrants.

Trump warned Sunday that if Harris wins the November election, “the entire country will be turned into a migrant camp.”

In an ABC News/Ipsos poll released Sunday morning, 46 percent of likely voters nationwide said they trusted Trump more than Harris on immigration. Thirty-six percent said they trusted Harris more.

In its advertising, the Harris campaign has seized on Trump’s opposition to the bipartisan legislation and promised she “will hire thousands more border agents” if elected. Trump continued criticizing the bill Sunday, saying he never needed legislation when he was president to “close the border.”

The Senate agreement earned the support of the National Border Patrol Council, a union of Border Patrol agents that is otherwise strongly aligned with Trump. The union’s past and current leaders spoke at Trump’s rally Sunday, urging voters not to believe Harris’s promise that she will secure the border.

During his remarks — which featured a backdrop of supporters waving signs reading, “Secure Our Border” — Trump brought at least a dozen Border Patrol agents onstage to make the union’s endorsement official. The group backed him in 2016 and 2020.

The CBP has already been offering generous incentives to address staffing shortages in recent months. The agency announced in January that new Border Patrol agents could be eligible for as much as $30,000 in incentives.

Last year, John Modlin, the chief Border Patrol agent in the Tucson sector, told a House committee that the Border Patrol needed about 22,000 agents to do its job. A May 2023 report from the Department of Homeland Security’s inspector general noted that “migrant encounters surged without corresponding growth in staffing” over recent fiscal years.

After he campaigned Saturday in solidly blue California, Trump’s Arizona rally took him to more friendly territory. The site of the event was in Yavapai County, where Trump defeated President Joe Biden in 2020 by nearly 30 percentage points.

Arizona is nonetheless a battleground state after Trump carried it in 2016 but narrowly lost it in 2020.

Trump’s latest Arizona stop came hours after the airing of a Trump TV interview where he suggested “radical left lunatics” could cause unspecified problems on Election Day that would need to be handled by the military. Harris’s campaign denounced the comments, saying they “should alarm every American who cares about their freedom and security.”

During the rally, Trump elevated his attacks on Harris and included multiple claims that are untrue or unsubstantiated. He repeated his assertion that she had never worked at a McDonald’s and the falsehood that she was the first Democrat to drop out of the presidential race in 2020.

He also accused Harris of being one of the “creators” of the campaign to defund the police, something she has never supported, though she has in the past broadly favored the notion of reexamining the relative money spent on law enforcement and social services. He also said she tried to abolish Immigration and Customs Enforcement, which is likewise untrue.

Trump inflated a false claim that Harris would raise taxes on “typical American families” by $3,000, up from a prior false claim of a $2,6oo increase. Harris has said she would not boost taxes on anyone earning less than $400,000.

Joseph Menn contributed to this report.

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