First Responders Partnership Grant Act of 2003 - Authorizes the Director of the Bureau of Justice Assistance to make grants to States (including the District of Columbia and U.S. territories), units of local government, and Indian tribes to support public safety officers (law enforcement and fire and rescue personnel) in their efforts to protect homeland security and prevent and respond to acts of terrorism. Sets forth minimum and maximum amounts for such grants. Declares that the portion of the costs of a program provided by a grant under this Act may not be more than 90 percent, with exceptions permitted in cases of fiscal hardship. Requires the Director to promulgate regulations to set forth procedures for requesting grants.