WASHINGTON—President Trump smiled as he entered the Roosevelt Room in the White House, armed with $16 billion in good news for farmers struggling amid his continuing trade conflict with China. By the time he left, Mr. Trump had effectively carpet bombed what little remained of his relationship with congressional Democrats by mocking House Speaker Nancy Pelosi’s intelligence, ridiculing her speaking style and calling the first woman to lead the U.S. House “a mess.”

Thursday brought another episode of the Donald Trump and...