The personal distaste could also be measured in body language, when European leaders made little effort to engage with Mr. Trump, chatting to one another while Mr. Trump walked along with the Turkish president, Recep Tayyip Erdogan, a semiauthoritarian outsider.

“Trump is becoming politically toxic in Western Europe,” Mr. Valasek said. “No one wants to be seen smiling with him after being berated on Twitter. Even more, Mr. Trump’s insults and his unpopularity among European voters make it harder for European leaders to do what he wants them to do, like increase military spending, even when they think they should do it.”

After Mr. Trump split with the Europeans on issues like climate change and the Iran nuclear deal, Mr. Valasek said, “leaders don’t want to be associated with anything he wants; it’s the kiss of death.”

They are also fearful of his populism, his support for Britain’s withdrawal from the European Union, or Brexit, and his affinity with their political adversaries, who share his nationalist, anti-immigration message.

Yet, Europe faces a dilemma with Mr. Trump, as Sigmar Gabriel, the former German foreign minister, said in an interview with Der Spiegel. “The truth is, we can’t get along with Trump and we can’t get along without the U.S.,” Mr. Gabriel said. “We therefore need a dual strategy: clear, hard and, above all, common European answers to Trump. Any attempt to accommodate him, any appraisal only leads him to go a step further. This must be over. From trade to NATO.”

He continued: “We cannot delude ourselves anymore. Donald Trump only knows strength. So we have to show him that we are strong.”

How to do that, however, is less clear, since Europe’s security dependence on the United States is both obvious and will not change soon, despite European talk of more money for a joint European defense.