Health Care for Veterans of Project 112/Project SHAD Act of 2003 - Makes a veteran who participated in a test conducted by the Department of Defense Deseret Test Center as part of a program for chemical and biological warfare testing from 1962 through 1973 (including the program designated as Project Shipboard Hazard and Defense (SHAD) and related land-based tests) eligible for hospital care, medical services, and nursing home care through the Department of Veterans Affairs for any illness, notwithstanding that there is insufficient medical evidence to conclude that such illness is attributable to such testing. Terminates such eligibility after December 31, 2005.