Building on Welfare Success Act of 2003

Building on Welfare Success Act of 2003 - Amends part A (Temporary Assistance for Needy Families) (TANF) of title IV of the Social Security Act (SSA) to revise, reauthorize, and extend the TANF program, with changes including the addition of grants to States for healthy marriage promotion programs.

Amends the Personal Responsibility and Work Opportunity Reconciliation Act of 1996 with respect to establishing national goals to prevent teen pregnancy.

Amends SSA title IV Part D (Child Support and Establishment of Paternity) to make various changes including providing for expanded enforcement.

Amends the Immigration and Nationality Act to make nonimmigrant aliens who fail to pay child support by more than $2,500 ineligible to receive visas and excluded from admission to the United States.

Provides for responsible fatherhood grants under SSA title IV part D.

Amends the Personal Responsibility and Work Opportunity Reconciliation Act of 1996 to give States the option to assist legal immigrant families.

Amends SSA title XIX (Medicaid) to provide for: (1) optional coverage of legal immigrants under Medicaid and SCHIP (SSA title XXI (State Children's Health Insurance) (SCHIP); and (2) a five year extension, and revision, of the transitional medical assistance program.

Provides authority under TANF for the use of TANF funds for housing benefits.