DES MOINES, Iowa — Roughly halfway between campaign kickoff and the first votes being cast, Sen. Kamala Harris is settling into a presidential campaign strategy that seeks to bridge what progressive and moderate voters are looking for.

There may be no better testing ground than Iowa, whose February caucuses will offer the first primary results in 2020. Iowa voters take their responsibility seriously, and Harris is investing heavily in the state.

The California Democrat recently wrapped up a five-day bus tour across Iowa, delivering versions of her stump speech that blend how she’d deal with the “3 a.m. thoughts” that keep Americans up at night with how she would “prosecute the case” against President Trump.

It’s a strategy that seeks to straddle the line between the progressive Democratic candidates who advocate sweeping structural change and moderates with a more incremental message. Ultimately, the idea is to convince Democratic voters that Harris and her hybrid candidacy would be their best bet against Trump.

While Vice President Joe Biden leads in polling and Massachusetts Sen. Elizabeth Warren has the strongest organization and palpable enthusiasm in the state, there are signs that Harris’ approach is starting to resonate. She has been running third or fourth in the state in recent polls, but Iowa’s caucuses have been to known to produce upsets.

“We’re building up momentum,” Harris told The Chronicle in an interview aboard her bus. “And that’s how it should be. I don’t want to peak overnight.”

Harris has not hesitated to brand herself as a progressive since arriving in Washington in 2017. Ahead of her presidential campaign, she released an autobiography that framed her career in law enforcement as one of a “progressive prosecutor,” a pre-buttal of sorts to progressives’ criticism that as San Francisco district attorney and California attorney general, she participated in a criminal justice system that disproportionately harmed people of color.

She has also embraced progressive policy positions, including being the first senator to co-sponsor Medicare for All legislation introduced by fellow candidate Sen. Bernie Sanders, independent-Vt., and cultivating a voting record that is among the furthest to the left in the Senate.

But in a field that includes Sanders and Warren, who are both running on the left end of the spectrum, Harris is sounding a more centrist note. Her Medicare for All plan, unlike Sanders’, would leave a place for private insurers and take longer for the transition. Her education plans include a focus on raising teacher pay and investing in historically black colleges and universities, with a narrower loan forgiveness plan than Warren’s or Sanders’. Her stump speech is designed to appeal to voters of all stripes, at times explicitly.

“The way I think about it is what I call the 3 in the morning thought,” Harris told one Iowa crowd. “For the vast majority of us, when we wake up thinking that thought, it is never through the lens of the party with which we are registered to vote. ... It is never through the lens of some simplistic demographic some pollster put us in.”

In the interview, Harris was dismissive of the notions of candidates’ “lanes.” She said she considers herself a “progressive Democrat” but that it’s “an abstract term” that people define differently.

Harris said she wants voters to think of her as “a problem-solving president ... trying to help transform their lives around the issues that are weighing on them.”

It’s a tactic that may be especially effective in Iowa, a state where voters are well aware that their first-in-the-nation caucus can shape the entire presidential primary season. Democratic caucus-goers make efforts to see the candidates in person, and experts familiar with the state say they are progressive but pragmatic.

Veteran Iowa Democratic strategist Jeff Link, who isn’t aligned with any of the candidates, pointed to the 2004 election cycle as a potential model for Harris. Months before the caucuses, Iowa polls showed the fiery progressive Howard Dean out in front. In the end, the winner was the more moderate John Kerry, who went on to win the nomination.

“They dated Dean and married Kerry,” Link said. “When pragmatism kicks in, I think voters are just not going to embrace the far left progressive lane. I think they’re going to look for somebody who can appeal to people in the Midwest and in rural areas, because those are the voters we need to swing back.”

But that doesn’t mean they aren’t looking for bold thinking, said Rachel Paine Caufield, a political science professor at Drake University in Des Moines.

“Iowa has this long and proud history of progressive reforms, civil liberties and civil rights,” Caufield said. “That’s a legacy that they intend to continue. On the part of Democratic caucus-goers, I think genuinely there’s an effort to understand how candidates see the world and how they think about basic issues of fairness and justice.”

Caufield said Harris’ message reminds her of Barack Obama’s in 2008, when he surged in the months leading up to the caucuses to pull off a victory over Hillary Clinton that vaulted him toward the nomination.

“It’s aspirational and inspirational,” Caufield said. “She’s really aiming for a big-picture vision expressing how she thinks about policy change, but she’s not getting into a lot of the details of her actual policy proposals on the campaign trail. And in that way, I think there’s a middle lane she sees for herself where she is super-likable and super-inspirational.”

Part of the assumption for all the campaigns is that front-runner Biden will falter. The moderate is leading in the polls but has been plagued by a series of gaffes on the trail, and Harris memorably attacked him in the first debate over his record on desegregation school busing. Emphasizing Harris’ toughness and ability to face off against Trump, the campaign hopes, will bring voters concerned about electability around to her.

Several Iowans interviewed on the campaign trail seemed to echo Harris’ messaging.

Larry Peterson, 73, a professor from Denison, Iowa, said he is looking for “somebody who inspires me and someone who is electable.” He was at the Iowa State Fair in Des Moines last weekend, wearing a Kamala Harris T-shirt and waiting to hear her speak.

“Somebody wants to promise the progressive dream, but they’ve got to get elected,” Peterson said. In 2016, he said, he was inspired by Sanders but couldn’t bring himself to vote for him because he feared the self-proclaimed democratic socialist would lose a general election.

Peterson said Harris, who attracted national attention in the Senate when she grilled Trump administration figures, including former Attorney General Jeff Sessions and Supreme Court nominee Brett Kavanaugh, is the candidate who can go “toe to toe” with Trump.

“We can’t afford four more years of Donald Trump,” added his wife, Eileen Peterson, also a 73-year-old educator. “We can’t afford to be wrong on the candidate we choose. So it’s a lot of responsibility.”

One positive indicator for Harris’ thread-the-needle strategy may be the way voters group her with other candidates. Few are decided but most have a top handful, and Harris’ name is just as likely to come up alongside Warren’s as it is that of a moderate like Mayor Pete Buttigieg of South Bend, Ind.

Many Iowa voters describe their decision-making process as more of a gut instinct than a policy deep-dive. With so many opportunities to see the candidates up close, they say they try to feel out what kind of people they are.

“She’s got a lot of integrity, she speaks well, she zeroes in on the issues, and she has a message that supports everybody, and so those are the core things I’m looking for,” said Harris supporter Phil Peters, a 58-year-old teacher from Des Moines who was attending one of her rallies. “There are a lot of candidates on the Democratic side that I think have great policy. I’m not sure they have what it takes to win the election, and so for me, I’m trying to separate out who has the staying power.”

His wife, Michele Senger, a 62-year-old teacher, was still making up her mind. She said she is looking for a candidate who has big ideas but can also get them done.

“I’m looking for people who are very articulate, who are very intelligent, that have policies and plans that seem reasonable and doable, and also seem like they have the kind of personality and fortitude who would be able to bring it forward and make it happen,” Senger said.

Voters said they did not enjoy watching the presidential debates, where the moderators often seemed to be coaxing the candidates into attacking each other.

“I prefer to listen to what they actually say about themselves, not to anything they say about somebody else,” said Jacki Bardole, 39, a sales and marketing director from Corning, Iowa, and an undecided voter who was listening to Harris at the state fair.

“I definitely appreciate that she’s not fighting against other Democrats — she’s fighting against the system,” Bardole said. “And I love that confidence, and the eloquence of her speaking is wonderful. And she’s right — the things that I worry about are the same things that you worry about, the same things that everybody worries about.”

Tal Kopan is The San Francisco Chronicle’s Washington correspondent. Email: tal.kopan@sfchronicle.com Twitter: @talkopan