The search for John McCain’s running mate is such a mystery that few people even know who’s in charge.

The Republican is leaning on a consummate behind-the-scenes player in Washington — attorney Arthur B. Culvahouse Jr. — for this maximum-discretion, minimal-disclosure assignment. In Culvahouse, a one-time White House counsel to President Reagan, McCain gets someone whose work mostly has been so obscure that he likely isn’t recognized outside Washington’s Beltway.