Shutdown Pay for Members of Congress Act of 2013 - Amends the Legislative Reorganization Act of 1946 to prohibit Members of Congress from receiving pay until a government spending agreement on future spending is agreed to by the House of Representatives and the Senate.
Makes such prohibition effective with the termination of a fiscal year at the end of which the House and Senate fail to reach agreement on government spending.
Directs the Committee on House Administration, consistent with the Constitution and the Anti-Deficiency Act, to consider the definition of "employing authority" under House Rules where Members of Congress would be deemed "non-essential."
Requires the amendments made by this Act to apply with respect to any adjustment which, but for this Act, would otherwise become effective in the event of a lapse in appropriations for government spending where the government would thereby shut down.