The construction of a massive new headquarters for the Department of Homeland Security, billed as critical for national security and the revitalization of Southeast Washington, is running more than $1.5 billion over budget, is 11 years behind schedule and may never be completed, according to planning documents and federal officials. In the aftermath of the Sept. 11, 2001, attacks, the George W. Bush administration called for a new, centralized headquarters to strengthen the department’s ability to coordinate the fight against terrorism and respond to natural disasters. More than 50 historic buildings would be renovated and new ones erected on the...