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.”