Brian Methe, an artist who lives in Cincinnati, had a thought. Wouldn’t it help the chances of his preferred presidential candidate, Hillary Clinton, if he were to design a simple, powerful image that could have the same effect as the “Hope” poster made by Shepard Fairey for Barack Obama’s 2008 run?

So Mr. Methe, 41, who has done graphic design work for the bands Wilco and the Avett Brothers, among others, created a rendering of Hillary Clinton that shows her in profile, with the slogan “I’m With Her” in the upper right corner. The color scheme is red, white and blue.

He was proud of what he had made, but when the image hit social media, the reactions from fellow adult males on Facebook were often angry:

“Does it come with darts?”

“I want the orange jumpsuit version.”

“I’ll use it as toilet paper.”

He should not have been surprised. As Mr. Methe said, being a white male Clinton supporter is “not a popular position,” something many polls have found as well. A New York Times/CBS News poll released on Sept. 15 showed that Donald J. Trump had the support of 57 percent of white males, while 33 percent supported Mrs. Clinton.

Within the white male demographic, 37 percent of those who are college-educated support Mrs. Clinton, versus 48 percent for Mr. Trump, according to an ABC News/Washington Post poll. Among white men without college educations, Mr. Trump’s lead is even greater: 76 percent to 17 percent.