MUSCATINE, Iowa — Eastern Iowa is home to industrial riverfront cities, small towns surrounded by verdant farmland and a consequential number of voters who were inspired to vote for both Barack Obama and Donald Trump.

And unlike many of the president’s Republican supporters, who could never imagine voting for a Democrat, many of these Obama-Trump voters are open to doing just that — meaning that Iowa counties along or near the Mississippi River, and similar ones throughout the Midwest, could once again be key to determining the next president.

“I voted for Trump — still not sure if it was the right decision,” said Tammy Faulkner, a 48-year-old convenience store clerk who lives in Louisa County in southeast Iowa and voted for Obama in 2008 and 2012. He seemed like a down-to-earth guy who would order a cheeseburger and fries, even if given fancier options, she said: “I have no qualms about voting either side, as long as they’re willing to do what it takes to get our country back to where we need it.”

Faulkner hasn’t been happy with some of the things Trump has done — namely, his comments about immigrants that she said “come across as racist” and the tariff war he started that could hurt the farmers who stop by her store for coffee — and she’s open to voting for a Democrat in 2020. But she has no idea whom that might be or even which of the 23 candidates might best align with what she’s looking for.

“In all honesty here,” she said, “lately I haven’t been paying a lot of attention.”

For many voters in this part of the state, that could be changing. Many of the candidates running for the Democratic nomination for president have focused heavily on eastern Iowa and counties that voted for both Obama and Trump, according to a map of visits curated by the Des Moines Register. This cycle, Iowa is not just a place where a single candidate can win the nation’s first nominating contest — it’s also where as a group they can demonstrate their ability to win back white working- and middle-class voters who defected to Trump in 2016 and played a substantial role in his election.

Nationwide, estimates show that between 5 and 15 percent of voters who picked Trump in 2016 had voted for Obama in 2012, or as many as 9.2 million voters. These Obama-Trump voters are one of the only voting groups to have had a significant change in their view of President Trump: In 2016, 85 percent of them held a “favorable” view of the president — a rate that fell to 66 percent this year, according to surveys conducted by the Democracy Fund Voter Study Group, a group of analysts and scholars from across the political spectrum who examine the evolving views of voters.

Winning the Iowa caucuses in 2008 put Obama on the pathway to the Democratic nomination — and winning the state in the general election was instrumental to him getting to the White House. But since Obama’s two victories here, Iowa politics have yo-yoed: In 2016, nearly a third of Iowa’s 99 counties flipped from having voted twice for Obama to voting for Trump, leading to Democrat Hillary Clinton’s defeat in the state. Democrats gained back some ground in Iowa in the 2018 midterm elections, winning three of the state’s four congressional seats, although the state elected a Republican governor.

More than half of Iowa’s 31 Obama-Trump counties continued to vote for Republicans in major races in 2018 while five counties reverted to voting for Democrats. Eight counties voted for Democrats for Congress and a Republican for governor.

As Trump headed to western Iowa on Tuesday for an event at a renewable energy facility and later to a private Republican fundraising event in West Des Moines, some of those hoping to replace him were trying to make their case to the east along the Mississippi River.

Following a state party dinner in Cedar Rapids, Sen. Bernie Sanders (I-Vt.) held a Sunday afternoon rally in Dubuque County, which swung from voting for Obama twice to voting for Trump in 2016, then swung back to voting for Democrats for Congress and governor in 2018. The next day, Sen. Elizabeth Warren of Massachusetts toured an ethanol plant in the next county over, and Sen. Kamala D. Harris of California met with voters in Dubuque and promised to improve the economy for all Americans, not just, as she put it, those with money in the stock market.

Meanwhile, former congressman Beto O’Rourke of Texas — who kicked off his candidacy in March with a tour of Obama-Trump counties along the Mississippi River — held a town hall in Clinton County, which Obama won with 60 percent of the vote in 2012 and Trump won with 48 percent of the vote in 2016, a year when voter turnout declined. In 2018, voters picked Democrats for the top two races on the ballot.

Former vice president Joe Biden held four events in the eastern part of the state, starting Tuesday in a county where Obama twice won with about 55 percent of the vote each time and Trump won with 57 percent. Biden has mostly brushed aside opportunities to appear with fellow candidates for the Democratic nomination, instead aiming to present himself as Trump’s direct challenger and the sort of candidate who could win back those voters who are no longer sure which political party best represents them.

Biden repeatedly attacked Trump’s policies and actions that he said have hurt American workers, including starting a tariff war with China, trying to undo the Affordable Care Act and not making education a priority.

Some in the party argue that trying to connect with Trump voters is a waste of time, as doing so could weaken their efforts to inspire, motivate and mobilize dedicated liberal voters — who are also more likely to vote in the Democratic primaries. But Democratic leaders in eastern Iowa caution that candidates should not forget the general election as they search for votes in the caucuses and primaries.

Kelcey Brackett, the Muscatine County Democratic Party chairman, noted that his county, like much of Iowa, has a high number of independent voters who refuse to align with a party, consider many politicians to be corrupt and would prefer an elected leader who is blunt and honest rather than politically correct. Obama won Muscatine County in 2012 with 57 percent of the vote, and Trump won in 2016 with 49 percent. Turnout was similar both years. In November, voters here picked the incumbent Democratic congressman, David Loebsack, and the Republican governor, Kim Reynolds.

Many of the Obama-Trump voters whom Brackett knows have told him they picked Obama and Trump — two presidents who could not be more different — because they hoped each represented transformational change.

“I think at least a good portion of them realize they need to consider another candidate” other than Trump in 2020, he said. “But I think that if we just have a mainstream Democrat, we’re going to miss some of those voters. We need someone at least interesting, someone who doesn’t fade into the crowd.”

Randy Naber, a retired elementary school teacher in Muscatine who sits on the school board, said that during the 2018 midterms “it was almost like pulling teeth” to get the Democratic gubernatorial candidate, Fred Hubbell, to visit the county — so he wasn’t surprised when Hubbell lost there. He said the best thing that presidential candidates can do is visit and talk with voters, and the local Democratic Party has set up a “welcoming committee” of sorts that will help any candidate organize an event and recruit a crowd. Nine candidates have visited the county so far this year, including Sanders, O’Rourke and Sens. Cory Booker of New Jersey and Kirsten Gillibrand of New York.

Naber has narrowed his list to four candidates he thinks can do well in places like Muscatine: Biden, Warren, Harris and Pete Buttigieg, the mayor of South Bend, Ind. He adds one more candidate he’s keeping an eye on: Sen. Amy Klobuchar of Minnesota.

An in-person visit is one way for candidates to try to break through Trump-dominated news cycles and insert themselves — or even just their names — into the social media feeds of Iowans.

Sitting at a Starbucks in Muscatine where his fiancee works, Eric Kortemeyer tried on Friday morning to name as many of the 23 Democrats running for office as he could but could only come up with two: Biden, whom he wants to get to know outside of “Obama’s shadow,” and Warren, whom he doesn’t know if he can trust, as he believes that she lied about having Native American heritage.

With some prompting, the 40-year-old food delivery worker added Sanders, who he said has some good ideas but is generally too extreme to get elected, and O’Rourke, although Kortemeyer wondered how much longer the Texan’s campaign will last. He has also heard about Andrew Yang on Facebook and likes the entrepreneur’s call for a universal basic wage.

Kortemeyer considers himself a Democrat and voted for Obama twice. Ahead of the 2016 election, he planned to vote for Clinton and was excited by the idea of having a female president. But then, he said, he started learning more about the attack on the U.S. mission in Benghazi and other criticisms of Clinton from people he met on Facebook who claimed to know the former secretary of state.

Meanwhile, he liked the idea of electing a businessman, although he was alarmed by some of the things Trump said during his campaign. Kortemeyer says he remembers thinking: “Oh, what the hell, let’s give this guy a chance.”

But Kortemeyer isn’t sure whether he will vote for Trump again. He disapproves of the president’s treatment of migrants at the border and what he sees as a reckless approach to foreign policy, and he thinks a border wall would be a waste of money. But he likes that the economy seems to be booming under Trump’s leadership.

He also likes that many Democrats want to make health care cheaper and easier to access, along with increasing the minimum wage — but he said he is starting to believe some of the things Trump says about Democrats not caring about working-class guys like him.

“Honestly, I don’t know what the hell I am anymore. I used to be a Democrat,” Kortemeyer said. “Do I want him to have a second term? I don’t know . . . I would vote for a Democrat, but they’re really going to have to convince me.”

Emily Guskin contributed to this report.