Mr. Obama did not specify who, exactly, was saying America should ignore its challenges.

Similarly, the next day in Los Angeles, Mr. Obama took on Wall Street and Washington, two of his favorite straw men. “I know some folks in Washington and on Wall Street are saying we should just focus on their problems,” Mr. Obama said. “It would be nice if I could just pick and choose what problems to face, when to face them. So I could say, well, no, I don’t want to deal with the war in Afghanistan right now; I’d prefer not having to deal with climate change right now. And if you could just hold on, even though you don’t have health care, just please wait, because I’ve got other things to do.”

Mr. Obama continued on the offensive against straw men that day in Los Angeles, pointing out that critics told him not to go on “The Tonight Show With Jay Leno” on NBC because “I can’t handle that and the economy at the same time.” Then, his audience primed, he delivered his standard kill line: “Listen, here’s what I say. I say our challenges are too big to ignore.”

And who can argue with that? Like most straw men, Mr. Obama’s are not complete fabrications. White House officials correctly pointed out that Senator Jon Kyl, Republican of Arizona, took a crack at Mr. Obama for appearing on the Leno show, saying that his “suggestion is that he come back, since he’s taken full responsibility, and get his people together” to confer on the budget.

But that is still a ways from the tortuous construct which Mr. Obama ended up with, that turned Mr. Kyl’s remark into one that somehow needed the “our challenges are too big to ignore” rebuttal, since it suggests that one of those challenges was apparently appearing on Leno.

“Here’s the trick: Take your opponent’s argument to a ridiculous extreme, and then attack the extremists,” said William Safire, the former presidential speechwriter who writes the “On Language” column for The New York Times Magazine. “That leaves the opponent to sputter defensively, ‘But I never said that.’ ”