The White House is ramping up an 11th-hour effort to build support for President Trump’s pick to lead the CIA, just days before she is scheduled to face a grilling from the Senate Intelligence Committee over her role in the agency’s controversial detention and interrogation program. For weeks, the CIA has led the charge on promoting now-deputy director Gina Haspel—a forward-leaning PR campaign that some critics have said is inappropriate for the clandestine agency. Only late last week did the White House stand up the kind of broad-based press campaign typical of other high-stakes nominations, issuing a swath of laudatory...