Donald Trump’s rallies once drew their share of benign conservatives, offbeat libertarians and plain curiosity seekers. But as time and Mr. Trump’s act have worn on, many of them have no doubt gone the way of his poll numbers. Mr. Trump’s crowds remain big and loud, but they’re angrier and more malevolent, and so is Mr. Trump.

At a rally on Wednesday near Fort Lauderdale, Fla., criticizing President Obama’s and Hillary Clinton’s records against the Islamic State, Mr. Trump said:

“In many respects you know they honor President Obama. ISIS is honoring President Obama! He is the founder of ISIS. He’s the founder of ISIS, O.K.! He’s the founder, he founded ISIS and I would say the co-founder would be crooked Hillary Clinton. Co-founder, crooked Hillary Clinton. And that’s what it’s about.” As the crowd erupted into cheers and chants of “Lock her up,” Mr. Trump then smiled and basked in the crowd’s applause.

Mr. Trump repeated the false charge on Thursday, saying he’d continue his inflammatory campaign, even if it meant losing in November.

A vast majority of Americans, of course, understand that Mr. Obama did not create ISIS, nor does the group, which targets Western nations, “honor” him or any other American leader. Some may even recall an ISIS beheading video released last year in which a masked jihadist stood before a bound, kneeling Kurdish soldier and declared: “Know, oh Obama, that we will reach America. Know also that we will cut off your head in the White House and transform America into a Muslim province.”