Sen. Ted Cruz sat down with a longtime ally in November at an office near D.C.’s Union Station to discuss the future of the Republican Party. Before long, the discussion touched on his own future. His friend Morton Klein, president of the Zionist Organization for America, told Cruz he believed that “Jew hatred and Israel bashing” was on the rise on the right — and that something had to be done about it. Cruz, who had begun a series of speeches decrying antisemitism in the GOP, told Klein he had been fielding requests from people urging him to run for...