“In my view, and McCain’s too, these guys at Breitbart are crackpots,” Mr. Salter said.

Another element of the speech — Mr. McCain’s gratitude for a life well lived — was equally important to the senator, Mr. Salter added, but it got lost in the media frenzy around the address.

Mr. Biden said he took the speech as a pointed message, if not to Mr. Trump, then to the nation. “I think he was delivering a message to the country, to his colleagues and to any of the opinion makers that would listen, and that is, ‘Look, this is serious stuff, our role in the world is not guaranteed, democracy is not guaranteed, we know how to do this and, damn it, we’d better focus and know what’s at stake.’”