Even at this late date in the Obama presidency, there is no surer way to elicit paranoid whispers or armchair psychoanalysis from Democrats than to mention the name Valerie Jarrett. Party operatives, administration officials—they are shocked by her sheer longevity and marvel at her influence. When I asked a longtime source who left the Obama White House years ago for his impressions of Jarrett, he confessed that he was too fearful to speak with me, even off the record. This is not as irrational as it sounds. Obama has said he consults Jarrett on every major decision, something current and...