Presidential Succession Act of 2002 - Provides for the President to designate: (1) the office of Speaker of the House of Representatives or Minority Leader of the House as the office that would discharge the duties of President if, by reason of death, resignation, removal from office, inability, or failure to qualify, there is neither a President nor Vice President; and (2) the office of Majority Leader of the Senate or Minority Leader of the Senate as the office that would discharge the duties of the President if at the time when the office designated under clause (1) is to begin to discharge such duties, there is no individual holding such office or the individual holding such office fails to qualify as Acting President.