When Representative Juan Ciscomani appeared onstage at a community center filled with banquet tables in Tucson recently to speak to high school seniors from underserved communities, he recounted his personal story of immigrating from Mexico as a young child, helping to support his family and eventually making it to Congress.

As he spoke about translating for his parents during school conferences and weekends spent washing cars to earn extra money to help support his family, Mr. Ciscomani made few mentions of the fact that he is a Republican — and no mention of his party’s presidential nominee, Donald J. Trump, who has made a political career of demonizing immigrants.

“I became a U.S. citizen in 2006 — 13 years after coming to this country,” Mr. Ciscomani told the crowd of community leaders interspersed with families of the young graduates, many of them first-generation Americans from some of the poorest parts of the city. “And then a member of the United States Congress 16 years later. So I believe in the American dream. I believe in the opportunities this country offers.”

It is a pitch that Mr. Ciscomani, 41, a first-term congressman, has leaned on since launching his first campaign for Congress in 2021 in a district that President Biden won the previous year, and is using again as he seeks re-election in one of the most competitive House races in the country.

The task has grown more complicated now that Mr. Ciscomani has a record to defend, including voting for an immigration crackdown measure that Republicans pushed through the House last year, which stalled in the Senate, and opposing a bipartisan bill that would have imposed tough new border enforcement policies and steered billions to funding them.

Those moves may have helped him fend off a primary challenge last month from a more right-wing Republican who had attacked Mr. Ciscomani as too moderate. But they could make his race tougher now that he has moved on to the general election, in which he will again face Kirsten Engel, a Democratic former state senator whom he defeated by fewer than 6,000 votes in 2022.

Mr. Ciscomani maintains that his message on immigration and his work on the issue in Congress resonate deeply in a district that lies along the U.S.-Mexico border. He says voters — including immigrants like him — understand the importance of enforcement and can distinguish between addressing illegal immigration and targeting immigrants indiscriminately.

“We have a border crisis,” he declared in his first campaign ad in 2021, in which Mr. Ciscomani is shown flipping through albums showing early childhood photos of him and his younger siblings both before and after they left Hermosillo, Mexico. His campaign applied a nearly identical template to his ads this cycle.

“People here in Arizona — we understand it because we grew up around it,” he said in an interview. “People know that we’re not talking about being anti-immigrant. We know that we’re not talking about the immigration process that I went through. This is not about that. This is about tackling the aspect of it that people are breaking the law.”

But critics note that the bipartisan immigration deal that Senate Republicans killed earlier this year — and that Mr. Ciscomani spoke out against — included a number of security measures that the G.O.P. had demanded. Mr. Trump torpedoed the measure to deny Mr. Biden a win on the issue and ensure that immigration would remain a potent issue throughout the remainder of the 2024 campaign.

The chief Republican negotiator for the bill in the Senate, James Lankford of Oklahoma, conceded in a recent interview with The New York Times that the bill was a victim of a fraught national political climate.

“Politics won out over policy — no doubt on that,” Mr. Lankford said, adding, “I honestly believe that exact bill would have passed in December, but by the time it got into February, it became immediately the major focus in the election.”

Mr. Ciscomani offered a different assessment of why the package had failed, saying it tried to solve too many issues at once.

Still, the Republican-written bill that Mr. Ciscomani voted for last year was a similarly sprawling package that addressed a wide range of issues. It would revive and codify a variety of border policies championed during the Trump administration, including construction of a border wall; the “Remain in Mexico” practice of keeping migrants who are seeking asylum either in detention facilities or on the opposite side of the border; and expedited deportation of unaccompanied children. It would also increase penalties for individuals who overstay their visas, as well as funding for more agents patrolling the border.

“If we really want to pass some kind of immigration deal or something, at the end of the day it’s going to have to be by different bites at the apple,” he said.

But Ms. Engel, who has mostly centered her campaign pitch on protecting reproductive rights, says voters are likely to reject Mr. Ciscomani’s message on immigration given his record in Congress.

“My opponent has been campaigning on the border and yet was presented with a bipartisan security deal and rejected it,” Ms. Engel said in an interview. “So you know, people are kind of fed up.”

Mr. Ciscomani has the added challenge of trying to distinguish his approach on the border — where he said he is trying to balance the imperative for strong security measures against the needs of small business owners who rely on a steady flow of migrant workers — with Mr. Trump’s highly negative message about immigrants and immigration.

During a visit on Thursday to a portion of the border just beyond Mr. Ciscomani’s district, Mr. Trump focused on the security threats he said immigrants posed, referencing a number of violent incidents while standing alongside relatives of people who the police say were attacked by undocumented immigrants. He also claimed repeatedly that migrants are taking jobs from minority communities, an assertion that has been widely disputed given that the number of foreign-born workers in the country is not large enough to offset the job creation in recent years.

Standing at a podium next to a portion of the border wall Mr. Trump has long championed, he said illegal crossings have “shattered so many families’ lives and stolen so many incredible young lives. And it’s also really badly hurt our Black population and our Hispanic population because these people are taking their jobs.”

It is a message in sharp contrast to the one embraced by Mr. Ciscomani, who said he hears often from companies that need more work visas to be approved more quickly so that more immigrants can work legally in the district.

“One thing that I realized when I got to Washington,” Mr. Ciscomani said, “is that people mix the border issue with all kinds of other issues.”