Global Security Priorities Resolution - Expresses the sense of the House of Representatives that: (1) the President should continue negotiations with other countries and unilateral initiatives to achieve nuclear arms reductions, and agree to the verifiable reduction of deployed U.S. and Russian nuclear weapons; (2) the Cooperative Threat Reduction (Nunn-Lugar) Program should be extended to requesting third countries; and (3) funds saved through nuclear arms reductions should be used for cooperative threat reduction and to alleviate problems affecting children and families that can contribute to support for international terrorism.