Veterans' Extended Health Care Services and Business Enhancements Act of 2003 - Amends Federal veterans' benefits provisions to: (1) extend through 2008 the period for the provision of veterans' noninstitutional extended-care services and required nursing home care; (2) remove a provision requiring a person to have been detained or interned for at least 90 days in order to qualify for outpatient dental care as a former prisoner of war; (3) allow any Under Secretary within the Department of Veterans Affairs (currently only the Under Secretary for Health) to provide business plans for the use within the Department of enhanced-use leases; (4) remove other statutory requirements with respect to the enhanced-use lease program; (5) allow the Secretary of Defense to make purchases through the Department's revolving supply fund; (6) provide for coverage under the tort claims laws for employees of Department nonprofit research corporations; (7) extend through 2008 the authority to establish such corporations; (8) revise due dates of certain required reports; and (9) designate the Department medical center in Prescott, Arizona, as the Bob Stump Department of Veterans Affairs Medical Center.