Fighting for American Jobs Act of 2006 - Directs each federal agency that provides grants, loans, or loan guarantees to businesses to require, as a condition of such assistance, that such businesses provide annually information on: (1) the number of employees employed in the United States and its territories and the number employed outside the United States, as well as wage information on U.S. employees; and (2) the percentage of the workforce that has been laid off or forced to resign during the preceding year. Prohibits, until the situation is corrected, subsequent federal assistance to businesses that lays off a greater percentage of workers in the United States or its territories than in other countries.