WASHINGTON—How business leaders talk about the Trump administration in private has been markedly different than what they are game to say in public. The dissonance was on full display here this week. 

Early on Tuesday, dozens of corporate executives and others assembled at a Yale CEO Caucus not far from the White House just as news emerged that the Trump administration planned to potentially double tariffs on steel and aluminum from Canada. Those in the room responded with a mix of groans and shocked laughter.