Ten days before HealthCare.gov opened for business, Marilyn Tavenner, the obscure federal bureaucrat whose agency oversaw the creation of the troubled online insurance marketplace, had a bad omen. It was a Sunday, and her mobile device was on the fritz, forcing her to go into the office. "It reminded me that I can still be brought to my knees by a malfunctioning BlackBerry," she joked in late September, recounting her technology woes to a group of insurance executives. Nobody at the Centers for Medicare and Medicaid Services, the agency Ms. Tavenner runs, is joking now.