McCurry served in the White House as press secretary to President Bill Clinton (1995-1998). He also served as spokesman for the Department of State (1993-1995) and director of communications for the Democratic National Committee (1988-1990). McCurry has also held leadership roles in several national campaigns, including national press secretary for the vice presidential campaign of Senator Lloyd M. Bentsen (1988), and spokesman and political strategist in the presidential campaigns of Senator John Glenn (1984), Governor Bruce Babbitt (1988) and Senator Bob Kerrey (1992). McCurry began his political career on the staff of the United States Senate, working as press secretary to the Senate Committee on Labor and Human Resources and to the committee's chairman, Senator Harrison A. Williams, Jr. (1976-1981). He also served as press secretary to Senator Daniel Patrick Moynihan (1981-1983).

McCurry is a principal of Public Strategies Group, LLC, a Washington, D.C.-based public affairs and strategic communications consulting firm, where he has practiced since leaving the White House. He also serves on boards or advisory councils for Share Our Strength, the Center for International Private Enterprise, the Council for Excellence in Government, the Junior Statesmen Foundation, the Wesley Theological Seminary, and the Woodrow Wilson School of Public and International Affairs at Princeton University.

McCurry received his bachelor of arts from Princeton University in 1976 and a master of arts from Georgetown University in 1985.