Presidents always deploy surrogates to appear on television to spout their talking points, but Mr. Trump has expanded on that by developing relationships with sympathetic media figures like Mr. Hannity who also serve as advisers. Mr. Hannity, the Fox News host, defends Mr. Trump's most controversial behavior in public, but privately, according to people close to Mr. Trump, he urges the president not to get distracted, and advises him to focus on keeping pledges like repealing the Affordable Care Act.