National Vaccine Injury Compensation Program Improvement Act of 2003

National Vaccine Injury Compensation Program Improvement Act of 2003 - Amends the Public Health Service Act to: (1) revise the basis for calculating the projected lost earnings of a person who sustained a vaccine-related injury; (2) increase the award for a vaccine-related death; (3) allow compensation for expenses for family counseling and establishing guardianship; (4) allow payment of interim attorneys' fees and costs; (5) establish a procedure for paying attorneys' fees; (6) extend from two to six years the statute of limitations for injuries or death from a vaccine set forth in the Vaccine Injury Table; (7) revise the membership and meeting schedule of the Advisory Commission on Childhood Vaccines; and (8) direct the Secretary of Health and Human Services to conduct a public service announcement campaign about the availability of the Program.Amends the Internal Revenue Code to increase the limit on Vaccine Injury Compensation Trust Fund administrative expenses.