Nuclear Regulatory Commission Continuation Act - Amends the Energy Reorganization Act of 1974 to permit any Nuclear Regulatory Commission (NRC) member appointed and confirmed before enactment of this Act, and not removed for cause by the President, to continue to serve until the earlier of: (1) the date on which the member's successor has been appointed and confirmed, or (2) the beginning of the first new Congress after the date on which the member's term expires.