Behind the brash, self-aggrandizing, and occasionally obnoxious exterior that Donald Trump presents to the world lurks a not entirely inconsequential level of intelligence and self-awareness. “I play to people’s fantasies,” he has said in explaining his business success, which is based, to a large extent, on the often blatantly false idea that anything with his name on it is bigger, better, more exclusive, and more glamorous than rival products. “I call it truthful hyperbole.”

When Trump entered Republican politics, which, increasingly, is the politics of reaction and resentment, he quickly grasped that making outlandish statements served a purpose in that arena, too, especially if his remarks were laced with vinegar. Indeed, he found that the bigger, badder, and meaner the persona he adopted was, the better he did in the polls.

Doubtless, this was welcome news to him. As anyone who has followed Trump’s career knows, he has always had very thin skin, which naturally inclines him to lash out at critics in the media and elsewhere who dare to question his claims. Now, it seemed, he could give vent to his inner nature and also do himself some good. Thus was born Trump the serial insulter, a political phenom who, for the past six weeks or so, has been sitting dandy atop the G.O.P. primary polls. Indeed, a new CNN poll shows that his level of support among likely Republican voters has crossed the thirty-per-cent mark. Apart from Ben Carson, another political neophyte, who was at nineteen per cent, the rest of the Republican candidates are all stuck in single figures.

The CNN poll was released shortly after Rolling Stone reported that Trump had said, in remarks directed at Carly Fiorina, the former chief executive of Hewlett-Packard and the only woman running in the G.O.P. primary, “Look at that face! Would anyone vote for that? Can you imagine that, the face of our next president?”

Trump’s comments about Mexican immigrants, John McCain, and Megyn Kelly, among others, have accustomed us to his outrageous and misogynistic statements. (He has twice retweeted someone who called Kelly, the star of Fox’s news division, a “bimbo.”) In the political world, indeed, there has been growing acceptance that Trump can get away with saying things that other candidates can’t; in some quarters, there was even reluctant admiration for how adeptly he was exploiting this advantage.

Until now, that is.

On Thursday, with very good reason, he was subjected to criticism from virtually every quarter, including from some Republican rivals who, earlier in the summer, had tried to ignore him. Jeb Bush called Trump’s remarks about Fiorina “small and inappropriate,” and said that he seemed intent on insulting his way to the Presidency. Bobby Jindal, the governor of Louisiana, called Trump an “egomaniacal madman who has no principles,” and said that it was time for him to return to reality television. On the Democratic side, Hillary Clinton said that Trump “seems to delight in insulting women every chance he gets.” Fiorina refused to respond directly, stating merely that, with her recent (if modest) rise in the polls, she seemed to be getting under Trump’s skin.

Trump, for once, seemed to be knocked off balance by all this. Initially, in an interview with CNN’s Chris Cuomo, he had suggested that Jann Wenner, the liberal publisher of Rolling Stone, had altered the article to make him look bad. “The writer actually called me and said, ‘I’m so upset, I wrote this great story and Jann Wenner screwed it up . . . because they added a lot of stuff, a lot of garish stuff, that I think is disgusting,’ ” Trump claimed.

Perhaps realizing that this story might not go over well, he provided an alternative explanation to Fox News, arguing that he had been talking about Fiorina’s “persona” rather than her physical appearance. “I say that about a lot of people,” he said. “I say, Look at that . . . . That’s not going to be our President!” Unfortunately for Trump, a quick glance at the article confirms that his remarks were surely directed at Fiorina’s appearance. The writer, Paul Solotaroff, was hanging out with Trump and some of his staffers on his private plane. They were watching the news and joshing around. This is Solotaroff’s description of the scene:

“When the anchor throws to Carly Fiorina for her reaction to Trump’s momentum, Trump’s expression sours in schoolboy disgust as the camera bores in on Fiorina. ‘Look at that face!’ he cries. ‘Would anyone vote for that? Can you imagine that, the face of our next president?!’ The laughter grows halting and faint behind him. ‘I mean, she’s a woman, and I’m not s’posedta say bad things, but really, folks, come on. Are we serious?’ ”

Later on Thursday, Trump tried out yet another line. Appearing once again on Fox News, he was confronted by a skeptical Greta Van Susteren, who said to him, “I don’t think you’re a first-time offender making a personal crack at a woman . . . the remark was about her face, and not about her persona.” This time, Trump suggested that he had been speaking not as a Presidential candidate but as an entertainer. “I did ‘The Apprentice’ and it was one of the top shows on television,” Trump said, adding, “Some comments are made as an entertainer and, as everybody said, as an entertainer is a much different ballgame.”

That it is, and the issue now is whether Trump will finally suffer some adverse consequences for breaking the rules of his adopted sport. One theory, expostulated in this week’s edition of The Economist, suggests that he won’t. “He says things that no politician would, so people think he is not a politician,” an article in the magazine said. “His supporters . . . think his boorishness is a sign of authenticity—of a leader who can channel the rage of those who feel betrayed by the elite or left behind by social change.”

Surely, there is something in this argument. Even angry Republicans, however, demand a certain level of civility in their Presidential candidates. Or, at least, Trump’s frantic efforts to divert attention from what he actually said about Fiorina suggest that they do. So does the rise in the polls of Ben Carson, who is civil to a fault. Trump, by contrast, just can’t seem to quit. Like a gambler on a lucky streak, he keeps doubling down. Unlike normal gamblers, however, he has appeared during his campaign to be playing with the odds loaded in his favor.

Maybe, just maybe, that is changing. When Trump made his remarks about Megyn Kelly having “blood coming out of her whatever,” there was at least some ambiguity about what he really meant. This time, there is none. Still, Trump won’t apologize. “What can I say, I’m leading with the evangelicals, I’m leading with women,” he said to Van Susteren. “I’m leading with African-Americans, with a very high number, and I’m leading with Hispanics, which is very interesting and I’m not surprised, because I’m gonna bring jobs back to our country.”