Protecting Children Against Crime Act of 2003 - Amends the Federal criminal code to provide that no statute of limitations shall apply for specified child abduction and sex offenses.

Amends the Jacob Wetterling Crimes Against Children and Sexually Violent Offender Registration Act to provide for the registration in the national sex offender registry of persons who produce or distribute child pornography.

Requires the Attorney General to carry out a program to provide grants to States for the development or enhancement of programs and activities for the support of AMBER Alert communications plans.

Directs the National Research Council of the National Academy of Sciences to study: (1) the extent to which Internet service providers can and do monitor Internet traffic to detect illicit child pornography sites; (2) the extent to which purveyors use credit cards to facilitate the sale of illegal child pornography on the Internet; (3) which credit card issuers have a system to facilitate the identification of such purveyors; and (4) options for encouraging greater reporting of such illicit transactions to law enforcement officials.