Jack Quinn, chief White House counsel, has submitted his resignation, an administration source confirmed. Quinn, who joins an exodus of White House staff members before President Clinton's second term begins, cited family reasons for his departure, the source said. As chief counsel, Quinn oversaw a wide range of legal matters that included helping devise the White House strategy for dealing with the various ethical controversies that have swirled around the Clinton administration. Quinn previously had served as chief of staff to Vice President Al Gore. He assumed the chief counsel job after the resignation of Bernard Nussbaum in March 1994.