DELAWARE, Ohio — Donald J. Trump is not popular in this prospering county north of Columbus. The Republican nominee’s dystopian language does not resonate here. Signs that read “Now Hiring” outnumber “Trump” campaign placards.
But many residents of this reliably Republican county, which last voted for a Democratic president in 1916, simply cannot imagine voting for Mr. Trump’s Democratic opponent, Hillary Clinton. And that goes a long way toward explaining why she has struggled to separate herself from Mr. Trump in this bellwether state.
“I just don’t know what I’m going to do,” said Anne Merrels, 48, who lives with her family in Powell, an old farming town that has sprouted a pair of farm-to-table restaurants at its crossroads.
The subdivisions of southern Delaware County are a world apart from the anger and decay of Ohio’s old industrial towns.
Here live the beneficiaries of globalization: Ohio State University professors, software engineers and bankers who work at the hulking JPMorgan Chase building, a structure on the southern edge of the county that is as large as the Empire State Building, though considerably shorter.
Delaware County’s median household income in 2014 was $91,936, by far the highest in the state and almost twice the statewide median income. The county’s unemployment rate was just 3.4 percent in July, compared with 4.9 percent nationwide.
Just as Mr. Trump has made inroads among Ohio’s blue-collar workers by promising to revive their fortunes, Democrats are hoping Mrs. Clinton can find new support among affluent and well-educated voters who are thriving in President Obama’s economy and may be wary of Mr. Trump’s bluster.
C. J. Soliday, a 46-year-old mental health therapist, said she was trying to persuade friends to vote for Mrs. Clinton by posing a single question. “People should ask if we’re doing better than we were doing eight years ago,” Ms. Soliday said. “And the answer is yes.”
Yet conversations with a few dozen voters here suggest that Mrs. Clinton faces considerable challenges in converting the distaste for Mr. Trump into support for her candidacy. Many of those who do not like Mr. Trump also dislike Mrs. Clinton. They are reluctant to cross party lines. And even here, there is still anxiety and pessimism about the health of the economy.
There are some like James Kehoe, a 40-year-old real estate agent and registered Republican, who said he did not recognize Mr. Trump’s descriptions of Ohio’s economic desolation and liked the idea of showing his two daughters that a woman could be president.
More common, however, are people like Ms. Merrels. She and her husband, a software engineer, went to see Mr. Trump in person this year at the convention center in Columbus. She was impressed by the long lines, but not by the speech. Mr. Trump, she said, seemed to talk mostly about polling numbers.
She said she had voted for the Republican nominee in each election since 1996. She said she would not vote for Mrs. Clinton, and was concerned that voting for a third-party candidate would amount to the same thing. But she is not reconciled to voting for Mr. Trump.
“I’d like someone to represent the United States who we are proud of, who we are not embarrassed by,” Ms. Merrels said.
Democrats remain hopeful that they can improve upon the 38 percent of local votes won by Mr. Obama in 2012. The Clinton campaign has opened an office on Delaware’s main street; the Trump campaign has also rented a storefront, but there is just a cardboard cutout of the candidate in the window.
Jenny L. Holland, a professor of politics at Ohio Wesleyan University, said she was watching with fascination as Democrats tried to make inroads in a place so Republican that Karl Rove, the Republican strategist, famously protested on national television in 2012 that the election should not be called for Mr. Obama until Delaware County’s votes were counted.
“What do you do if the Republican candidate is unpalatable to you?” asked Professor Holland, who also lives in the county. “Do you just show up and not vote for president at all? Or — gasp — could there be a possibility that a Republican woman would show up and vote for Hillary Clinton? We just don’t know.”
Delaware County was mostly farmland until a few decades ago, with a modest cluster of factories in the county seat. Roger Marksch, 67, built and fixed machines in those factories for almost 50 years before hanging up his tools last year. He watched as the factories closed or moved to Japan, China, Mexico and Finland. “I got out just in time,” he said with a laugh.
But even as those jobs faded away, developers were replacing Delaware’s soybean fields with subdivisions. Columbus was growing rapidly, fueled by a modern mix of government, education and financial services. Commuters doubled the suburban county’s population from 1980 to 2000, and it is on pace to double again by 2020, easily topping 200,000.
John Kasich, Ohio’s governor, is the archetypal local Republican with misgivings about Mr. Trump. Mr. Kasich, who lives in Delaware County’s southern tier, not far from a planned Ikea, has repeatedly rebutted Mr. Trump’s bleak descriptions of Ohio’s economy. He has not offered an endorsement.
Others said they were concerned Mr. Trump was insufficiently conservative. Craig Johnson, who owns a pizzeria in the county seat, said he doubted that Mr. Trump was a Republican, but he laughed when asked if he would consider Mrs. Clinton. “Listen, I’m a 45-year-old small-business owner in Delaware, Ohio, and I like guns, fishing and Nascar,” he said.
He is mulling a vote for Gary Johnson, the Libertarian nominee.
For a while after the recession, regular customers who bought half a dozen cigars each week had cut back to three or four. Lately, they are buying half a dozen. He recently bought his first new vehicle since 1999, “the last time things were decent.” He is not particularly moved by Mr. Trump’s promises of an economic revival.
But Mr. Paxton said he still planned to vote for Mr. Trump for standard Republican reasons: He wants lower taxes and less regulation. He is upset about an excise tax of 40 cents per cigar imposed in 2009 to fund a children’s health insurance program, and he is upset about a ban on providing tobacco samples to his customers.
Matt Lester, 37, a graphic designer, was blunt: “He wasn’t my first, second, third or fourth option, but he is better than Hillary.”
Indeed, as in other parts of Ohio, Mrs. Clinton faces some challenges in maintaining the support of her traditional base.
Shalyn Shelton, 26, has completed one and a half years of courses toward a nursing degree, but she already owes $22,000 in student debt and she cannot afford to continue. She also cannot afford to live in Delaware, where she grew up, so she recently moved with her partner to Marion, 20 miles north.
And on a recent afternoon she sat outside the International Paper factory where she had worked for the last two years, because she and her co-workers have been on strike since May.
The factory, which cranks out diaper boxes, egg crates and other corrugated containers, offers some of the best jobs still available in Delaware for people without college degrees. Ms. Shelton makes about $21 an hour stacking boxes. And business is booming.
But International Paper wants the workers to accept more mandatory overtime rather than hire more workers. So Ms. Shelton sat among her fellow workers, holding a cardboard sign that read, “84 Hours a Week = No Family! No Church!” In her arms she cradled her daughter, nearly 3 months old.
Mrs. Clinton has framed her presidential campaign as an effort to help people like Ms. Shelton. She has proposed making college free for people under a certain income, creating more affordable housing, strengthening collective bargaining, and improving benefits for working parents. She has won the endorsement of Ms. Shelton’s union, the Teamsters.
But Mrs. Clinton has not won the support of Ms. Shelton, who has not registered to vote and does not plan to do so. “They don’t care about us,” Ms. Shelton said of Mr. Trump and Mrs. Clinton.
A few minutes later, she opened the door at least a crack: “I’ll tell you what — if she shows up here, she would have my vote.” (Editor’s note: She did not, but Trump did have a rally at the Delaware County Fairgrounds.)
A version of this article appears in print on September 10, 2016, on page A1 of the New York edition with the headline: Ohio County Spurns Trump but Is Cool to Clinton.