As they watched Mr. Trump clinch his third straight victory with a win in the Nevada caucuses last week, Mr. Rubio and his aides concluded that the only way to beat him was to get inside his head, by stooping to his level: Taunt, insult, mock and have a blast doing it.

They seem satisfied that it is working.

“We came to the conclusion that if being a part of the circus is the price you have to pay in order for us to ultimately be able to talk about substantive policy, then that’s what we’re going to do,” said Todd Harris, a senior Rubio adviser.

Mr. Harris noted that Mr. Rubio’s speeches were now being carried live on television. And if the price of admission, he added, was talking about “how Trump is a con man, with a bad spray tan,” so be it.

What has followed is a race that looks more like a variety show than a campaign to elect the most powerful leader on earth.

So far, Rubio supporters seem surprised by, if open to, his change in tone.