One Democratic strategist said that shortly after an appearance on Fox he got a phone call from a White House official telling him not to be a guest on the show again. The call had an intimidating tone, he said.

The message was, “We better not see you on again,” said the strategist, who spoke on condition of anonymity so as not to run afoul of the White House. An implicit suggestion, he said, was that “clients might stop using you if you continue.”