Gov. Ron DeSantis of Florida takes questions from voters at every campaign stop, so he often faces variations of the same question — sometimes several times in a single day at different events scattered hundreds of miles apart.

And he seems to be growing tired of one frequently asked question in particular: Why doesn’t he more directly attack former President Donald J. Trump?

It came up again Wednesday at a community center in Waukee, Iowa, where Christopher Garcia, a 75-year-old retired gas serviceman, pressed Mr. DeSantis in a lengthy back-and-forth.

Mr. DeSantis responded that, well, he does criticize Mr. Trump, who is leading the Republican presidential field by a wide margin.

“I’ve articulated all the differences time and time again on the campaign trail,” the Florida governor said. He accused the news media of wanting the Republican candidates to “smear” each other with personal attacks. “That’s just not how I roll,” he added.

It is true that Mr. DeSantis often enumerates what he says are Mr. Trump’s failures to keep the promises he made as a candidate in 2016 once he got into office. But Mr. Garcia was asking Mr. DeSantis something deeper and more personal: Did he think Mr. Trump’s often vulgar language and crass insults — such as mocking Carly Fiorina’s physical appearance and belittling John McCain’s military service — made him unfit for the White House?

“The guy has no class,” argued Mr. Garcia, who said he had nonetheless voted for Mr. Trump in 2016 and 2020.

Mr. DeSantis declined to offer his own opinion on Mr. Trump’s conduct. But if Mr. Trump were to win the Republican nomination, Mr. DeSantis said, “the whole election will be a referendum on his behavior.” He then returned to listing Mr. Trump’s unfulfilled campaign pledges.

Mr. Garcia, sitting in a plastic chair with his walker leaning against his knees, raised his hand again, hoping to continue the conversation. But Mr. DeSantis did not return to him.

How, and even whether, to attack Mr. Trump is a challenge that all of the former president’s rivals have struggled to surmount. As of yet, no approach seems to be working that well.

Former Gov. Chris Christie of New Jersey is attacking Mr. Trump most aggressively, in terms both political and personal. But Republican voters have shown little appetite for his message.

Nikki Haley, the former United Nations Ambassador now widely seen as Mr. Trump’s nearest challenger, takes only carefully calibrated shots at the former president. But her recent rise in the polls may have as much to do with her crossover appeal to Democrats and independents as with her cautious approach to Mr. Trump. And Vivek Ramaswamy, the entrepreneur who is quick to attack the rest of the field, has lavished praise on the former president, leading some voters to question why he is running at all.

So far, Mr. DeSantis and Ms. Haley, and their allied outside groups, have spent far more money attacking each other than Mr. Trump.

After the DeSantis event wrapped up, reporters swarmed Mr. Garcia for interviews, reflecting both the heightened attention on the Iowa caucuses, which take place on Jan. 15, and what seems to be one of the core issues confronting Mr. DeSantis’s campaign.

Mr. Garcia, who lives outside Des Moines, said he planned to caucus for Mr. DeSantis, although he would vote for Mr. Trump in a general election. He was not impressed with the governor’s critiques of Mr. Trump on Wednesday, calling them “vague.”

“Are these people afraid to take Trump head on?” Mr. Garcia said of Mr. DeSantis and the other candidates. “I mean, is that the problem?”

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