Government Contractor Accountability Act of 2013 - Requires specified federal agencies (defined as establishments by the Inspector General Act of 1978) to report to Congress on their response, or lack of response, to covered final audit reports submitted to such agencies by an Inspector General or by the Special Inspector General for Afghanistan Reconstruction or the Special Inspector General for Iraq Reconstruction. Defines "covered final audit report" as a final report issued by an Inspector General that includes a recommendation for implementing cost-saving measures or for seeking reimbursement for failure by a contractor or subcontractor to successfully complete a contract due to poor performance, cost-overruns, or other reasons that would, if implemented, result in at least $2 million in savings.