NEW ORLEANS — In the busy and under-staffed offices of New Orleans’ flood-control leaders, there’s an uneasy feeling about what lies ahead.

By the time the next hurricane season starts in June 2013, the city will take control of much of a revamped protection system of gates, walls, and armored levees that the Army Corps of Engineers has spent about $12 billion building. The corps has about $1 billion worth of work left.