Dempsey is the former general manager of The Columns Banquet and Conference Center in St. Charles, MO. He is a member of the St. Cletus Catholic Church, the St. Charles and St. Peters Chambers of Commerce, and the St. Charles Rotary Club. He is a former member of the St. Charles City Council. In 2000, Dempsey was first elected to the Missouri House of Representatives, winning reelection in 2002, 2004 and 2006. He is the chairman of the Special Committee on Parliamentary Procedure, and also serves as the chair of both the Ethics and Rules committees. Dempsey was elected to the Senate in a 2007 special election previously serving as Majority Floor Leader in the Missouri House of Representatives. In January of 2012, Dempsey was elected as President Pro Tem of the Missouri Senate. In 2012, Dempsey was elected as President Pro Tempore of the Missouri Senate. He still serves as President Pro Tem, and is also Vice President of First National Bank of St. Louis.
Dempsey was born to restaurant owner Ernest "Ernie" Dempsey and Peggy Pedrucci, along with younger sisters Anne and Mary. He lives in St. Charles, Missouri, with his wife Molly. They have three children: Meaghan, Abby, and Jack, and a dog, Bazzel.