National Center for the Right to Counsel Act This bill establishes in the District of Columbia a private, nonprofit corporation to be known as the National Center for the Right to Counsel to provide: (1) financial support to supplement funding for public defense systems that provide legal assistance to indigent defendants, and (2) financial and substantive support for training programs to improve delivery of legal services to indigent defendants. The bill requires each state to have a state advisory council to: (1) monitor, receive, and investigate complaints regarding the compliance of public defense systems that receive funding with applicable laws and regulations; (2) notify the center of any apparent violations; and (3) collect data on the delivery of public defense services and facilitate information sharing among the state's public defense systems. The center must make available to the public an online database that includes the contact information for all public defense systems in every state. The bill requires the center to establish regional backup service centers to assist public defense systems with access to investigators, sentencing mitigation specialists, and information about available grants. The Government Accountability Office must complete a study four years after this bill is enacted about the effects of the center on providing public defense services and on the cost of the criminal justice system.