National Intersection and Interchange Safety Construction Program Act of 2019 This bill directs the Department of Transportation (DOT) to establish a national intersection and interchange safety construction grant program. Under the program, DOT may make grants to governmental entities and planning organizations to assist a project that is eligible for federal-aid highway funding and will improve the safety of intersections or interchanges on the National Highway System that are used by an average of 50,000 vehicles a day and are in immediate need of safety improvement.