Some people who have less at stake are going on the record to support Mr. Frazier’s stance against the president. Tom Glocer, the former chief executive of Thomson Reuters, wrote on Twitter on Monday: “Ken has stood up for true American values. I call on all other members of Trump’s image-burnishing committees to do the same.”

Privately, many chief executives say they are fuming, outraged by the president. (This after many of them campaigned to get on Mr. Trump’s committees.) But many are too scared to say anything publicly that could make them or their company a target of Mr. Trump’s wrath.

Indeed, Mr. Trump’s vitriol against Mr. Frazier and Merck — a company that depends on the government as a buyer for many of its drugs — will perhaps have an even greater chilling effect on other C.E.O.s who may consider speaking out. (The potential for economic retribution against Merck also demonstrates just how brave Mr. Frazier was in taking a stand.)

When I asked one chief executive Monday morning why he had remained publicly silent, he told me: “Just look at what he did to Ken. I’m not sticking my head up.” Which, of course, is the reason he said I could not quote him by name.

The same trepidation may explain why people like Mr. Ogunlesi don’t say anything. He runs an infrastructure fund that will most likely have to do business with the federal government. And Ms. Nooyi’s PepsiCo, for example, was briefly boycotted by Trump supporters when she made some comments that were construed as critical of him.

Other C.E.O.s, like Jamie Dimon of JPMorgan Chase, have contended that they consider it part of their patriotic duty to remain on the president’s business council, even when they disagree with things Mr. Trump says or does.

“It is very hard if you say, I’m going to go off an advisory group or not do A-B-C, because you disagree on one issue,” Mr. Dimon said in early June after Mr. Trump withdrew from the Paris climate agreement, a move that Mr. Dimon was against. Elon Musk of Tesla and Robert Iger of Disney resigned from the council in protest.