Stay in Place, Cut the Waste Act of 2013 - Requires the Director of the Office of Management and Budget (OMB) to: (1) review and report on the extent to which federal agencies have reduced travel expenses by the use of video conferencing pursuant to Executive Order 13589 and OMB Memorandum 12-12-12; (2) develop a plan for fiscal years beginning with FY2017 to use video conferencing to achieve the lesser of a 50% reduction in federal agency travel expenses below FY2013 levels, or the greatest reduction in such expenses that the Director considers feasible; and (3) rescind amounts made available for travel expenses that are proposed for reduction under this Act.