She has called him a “moron.” He has mused publicly — purely in jest, his aides later insisted — about wanting to hit her with the oversized wooden gavel used to keep order in the House. The relationship between Speaker Nancy Pelosi and the man who is most likely to succeed her should Republicans win control of the House in next month’s elections is barely civil. And as the moment of the possible succession draws closer, she has become less and less interested in masking her contempt for Representative Kevin McCarthy of California, the top Republican. At a news conference last week, when asked to respond to Mr. McCarthy’s claim that she was not allowing Democrats to speak out about what he described as a crisis at the border, Ms. Pelosi said of the minority leader, “I don’t even know what he’s talking about — and I don’t know if he does.” The same week, her spokesman, Drew Hammill, savaged Mr. McCarthy for a news conference he had held on the steps of the Capitol to discuss “firing Nancy Pelosi.” It was, Mr. Hammill said, “about par for the course for an uninspiring and incoherent politician like the minority leader, whose only real accomplishment to date is typing up a radical right-wing wish list that sends a clear message to the American people that House Republicans have gone off the deep end.” And that was the edited version.