Keith Mann, a self-described independent voter, sat out the 2024 election, dismayed by both candidates for president.

He still does not care for President Trump’s character. But more than a month into Mr. Trump’s second term, Mr. Mann, a 41-year-old Phoenix resident, said he was cautiously optimistic about what he had seen so far.

“He’s doing what he said he would do,” Mr. Mann said. He was encouraged by reports of fewer migrants crossing the border, in favor of reducing aid to Ukraine and hopeful that Elon Musk would root out excessive government spending and, “like Robin Hood,” deliver the savings to citizens in the form of $5,000 dividend checks.

“I’m just waiting to see how it pans out,” Mr. Mann said. “At the end of the day, he’s our president — you can’t just wish him bad.”

As Mr. Trump prepares to address a joint session of Congress on Tuesday evening — a stand-in for the State of the Union during a president’s first year in office — voters in battleground districts around the country are trying to make sense of the frenzy of executive orders and other actions that have so far defined Mr. Trump’s second term.

In Arizona’s First Congressional District, around the swingy suburbs of Phoenix and Scottsdale — areas that helped flip Arizona blue in 2020 before shifting rightward again last year — reactions to Mr. Trump ranged from elation among Republicans to disgust among Democrats, with a few wary independents wedged in between.

The partisan rancor in this competitive district remains high, but, in conversations with several dozen voters across the political spectrum, many seemed willing to give Mr. Trump the runway he needs to execute his “America First” vision of the country.

“I feel great,” said Rashad Davis, 33, a Republican who was particularly enthused about the import tariffs Mr. Trump has announced. “He’s sticking to his word — everything he said.”

Many voters singled out the so-called Department of Government Efficiency, Mr. Musk’s cost-cutting effort, as a major driver of their open-mindedness toward the Trump administration — at least, to a point.

Maureen Wielgus, 69, said that she had voted for Mr. Trump in each of the last two elections and that she was pleased with his performance so far, though she added that he needed “to soften his approach a bit sometimes.”

Ms. Wielgus had similarly qualified praise for Mr. Musk’s initiative, which has fired thousands of workers and boasted of tremendous government savings, often only to backtrack and delete its mistakes.

“They’re going in like a bulldozer, a little firm,” she said. “But they’re finding the corruption and the fraud.”

Around the state, Arizonans seemed to be split on Mr. Trump. Recent polling there has found that roughly half of the state’s residents at least somewhat approve of his handling of the job. Rich Thau, the president of the nonpartisan research firm Engagious, said that, in a recent focus group of a dozen Arizona residents who voted for Joseph R. Biden Jr. in 2020 before switching their support to Mr. Trump last year, all of the people gave Mr. Trump high marks for his performance.

“They want somebody who’s a strong leader, who takes command, does what he says, and that’s what they feel like they’re getting when they see Trump in action,” Mr. Thau said. But, he added, “they are very concerned about his getting distracted.”

Dan Hylen, 39, an independent who did not vote last November, said he had seen “some good and some bad” from Mr. Trump so far.

“Some of the government efficiency stuff I feel like is maybe going in the right direction,” he said. “I like the idea of cutting the fat.”

But he disliked Mr. Musk’s “willy-nilly, shoot-from-the-hip attitude,” and was not in favor of Mr. Trump’s approach to Ukraine. “I don’t want to be in every single war in the world,” Mr. Hylen said, “but I think we have to help some people out sometimes.”

Some voters said Mr. Trump’s combative showdown with President Volodymyr Zelensky of Ukraine on Friday, in which he angrily rebuked Mr. Zelensky for not showing sufficient gratitude for the United States’ support of Ukraine in its war against Russia, was a shameful display.

“It’s an embarrassment,” said Greg Wise, 53, who votes Democratic. “Throwing away decades of good will with neighbors.”

Others saw it as the perfect representation of a foreign policy agenda that prioritizes American interests.

“He’s showing that we’re not messing around,” said Tasha K., a Republican from Scottsdale who declined to give her last name out of fear that her husband, who is a federal employee, would face retribution. “He put America first, and that’s what we hired him to do.”

The First Congressional District’s ambivalence toward Mr. Trump could be seen recently in moments beyond conversations with voters.

On Monday, Democratic groups organized a protest on a busy street corner in the district, accusing Mr. Trump and the district’s Republican representative, David Schweikert, who voted for a budget resolution last month that calls for deep cuts to government spending, of neglecting their interests. Protesters held up signs reading “Fire Musk,” as well as images of a “missing” Mr. Schweikert on a milk carton. Many passing drivers honked in support, while others rolled down their windows to voice their dissent.

Still, in a purple district where voters of different political stripes frequently brush up against one another, even some of the president’s steadfast opponents were willing to look for silver linings.

Nina Meixner, 71, said she was a conservative who had backed former Vice President Kamala Harris last year because she disliked Mr. Trump’s personality. But she was encouraged by his tough stance on immigration and the tariffs he was putting into effect.

Ms. Meixner cringed at the chaos that she said was Mr. Trump’s “business model.” But, she added, “there’s things that I am happy for.”