Fleischer was born in Pound Ridge, New York. He graduated from Middlebury College in Vermont in 1982. He worked as press secretary for Congressman Norman Lent. Fleischer was Senator Pete Domenici's press secretary from 1989 to 1994. He served as spokesman for the House of Representatives Ways and Means Committee for 5 years. Late he was deputy communications director for George H. W. Bush's 1992 reelection campaign, then communications director for Elizabeth Dole. He joined George W. Bush's Presidential Campaign in 1999.
On May 19, 2003 he announced that he would resign during the summer, citing a desire to spend more time with his wife and to work in the private sector. He was replaced by deputy press secretary Scott McClellan on July 15, 2003.