State Budget Relief Act of 2003 - Requires the Federal medical assistance percentage (FMAP) under title XIX (Medicaid) of the Social Security Act (SSA) for: (1) a State for FY 2002 to be substituted for the State's FMAP for each of such covered calendar quarters if the FMAP determined for a State for a covered calendar quarter would otherwise be less than the FY 2002 FMAP; and (2) each eligible State for each covered calendar quarter to be increased by two percentage points. Mandates specified FMAP increases for States with high unemployment rates, and a specified Medicaid payment cap increase for territories. Prohibits application of the FMAP increases for a State under this Act with respect to: (1) disproportionate share hospital payments under Medicaid; and (2) payments under SSA titles IV and XXI (State Children's Health Insurance) (SCHIP).