Iran Sanctions Enhancement Act - Amends the Iran Sanctions Act of 1996 (ISA) to require: (1) the President to initiate an investigation into the possible imposition of sanctions against a person immediately upon U.S. receipt of credible information indicating that such person may have violated ISA; (2) the Government Accountability Office (GAO) to publish a monthly list of potential ISA violators; (3) the President to initiate an investigation of ISA violators based upon GAO information if an investigation has not already been initiated; and (4) the President to complete such investigation within 45 days and notify Congress of any person found in violation of ISA.