Mr. Miller is a consistent immigration restrictionist, opposed to legal and illegal arrivals, and when Mr. Miller has his ear, so is the president. But in his last State of the Union address, Mr. Trump blurted out — off script — that he wanted more legal immigrants than ever. Tellingly, when the border crisis first flared up last year, the White House zigzagged on its response. Was separating families at the border an intentional policy meant to deter further immigration or a regrettable result of something Democrats had done? Mr. Trump has been all over the map on the question. But Mr. Miller said it was intentional, while Ms. Nielsen insisted that it was outrageously "offensive" to suggest the administration would ever use family separation in such a punitive fashion.