The Reclamation Rural Water Supply Act of 2003 - Authorizes the Secretary of the Interior to carry out a rural water supply program in Reclamation States.

Directs the Secretary to develop and publish in the Federal Register criteria for determining the eligibility of a water supply project for assistance under this Act, including: (1) whether a project serves rural areas or Indian tribes; (2) whether there is an urgent need for a project that would result in continuous, measurable, and significant water quality benefits, address current or future water supply shortages, or improve the health or aesthetic quality of water; (3) whether a project helps meet any applicable legal requirements; (4) whether a project promotes a regional perspective to water resource management issues, implements an integrated resources management approach, increases water management flexibility, or forms a partnership with other entities; and (5) whether a project provides benefits outside the region in which the project is carried on.

Authorizes the Secretary to: (1) conduct appraisal investigations of proposed rural water supply projects; and (2) carry out feasibility studies of proposed rural water supply systems.

Requires State and local authorities, Indian Tribes, or other entities carrying out rural water supply projects under this Act to demonstrate the ability to pay all operation, maintenance, and replacement costs of such projects.