Then there was an interview with Valerie Jarrett, one of Mr. Obama’s senior advisers. Ms. Jarrett was asked why some voters had the impression that the president was attacking the rich. “Well, they may be watching one particular network,” she sniffed. “CNN?” the interviewer teased.

None of this has gone unnoticed inside the studios and executive suites of Fox News, which is rebuffing these White House put-downs as a denigration of the presidency.

“I think it lowers the office,” Michael Clemente, Fox’s executive vice president of news, said in an interview on Wednesday. “For it to come up as regularly as it does — and it’s not every day but every other week, I’d say — it’s just unusual. Especially given the issues out there, like the lack of new jobs and Syria.”