Rosenbaum was born in Toledo, Ohio and attended Whitmer High School, the middle child of three brothers. His father, Marvin Rosenbaum, was a furniture salesman and later the owner of a premiums and incentives distributor, and his mother, Edith Millman Rosenbaum, was a vice president at a local advertising agency. Rosenbaum graduated from Harvard College in 1974 with an A.B. in Government. He received a joint Juris Doctor and Master of Public Policy from Harvard Law School and Harvard Kennedy School in 1978. At Harvard Law he was a member of the winning team in the 1976 Ames Moot Court Competition. Rosenbaum is married to Marti Radlo Rosenbaum, and has three grown children and two grandchildren.
Policy debate
At Harvard, Rosenbaum was a member of the winning team at the 1974 collegiate National Debate Tournament. In 1979, he was one of the coaches for Harvard's National Debate Tournament-winning team. Rosenbaum and his debate partner Charles Garvin were voted the second-best policy debate team of the 1970s in a poll of contemporary debate coaches and participants. Rosenbaum serves on the board of directors of Harvard Debate, Inc, and is a former trustee and chair of the National Debate Tournament. In 2011, Rosenbaum was named to the board of directors of the National Association for Urban Debate Leagues.
Business
Rosenbaum is currently the president of Palisades Associates, Inc., a Bethesda, Maryland-based private equity firm. He was previously a consultant with the Boston Consulting Group and a vice president of buyout firm Dyson-Kissner-Moran. In 1987, Rosenbaum was one of the five founders of the Carlyle Group. He left within the first year. From 2003 to 2010, he was the Chairman of TVC Communications, LLC, a distributor to the broadband industry, until its purchase by WESCO International. From 2003 to 2012 Rosenbaum was the Chairman of Empire Kosher Poultry, Inc., the largest producer of kosher poultry in the United States, and from 2006 to 2012 he was the company's chief executive officer. In 2014, Rosenbaum was one of the lead investors in a group that purchased the Dayton Dragons, the Class A minor league affiliate of the Cincinnati Reds, from Mandalay Sports Entertainment. In 2016, Rosenbaum purchased a minority interest in the Mahoning Valley Scrappers, the Class A-Short Season minor league affiliate of the Cleveland Indians.
In 2011, the Metropolitan Council on Jewish Poverty granted Rosenbaum its Humanitarian Award. As the CEO of Empire Kosher, Rosenbaum oversaw the donation of kosher food products to community food pantries. In 2009, the Philadelphia Jewish Labor Committee granted Rosenbaum, along with U.S. Senator Bob Casey, a Labor Human Rights Award. In 2007, the Jewish Labor Committee granted Rosenbaum a National Trade Union Council for Human Rights Award. Rosenbaum is a past board member of the United States Olympic and Paralympic Foundation, which supports the United States Olympic and Paralympic teams, as well as the USA Swimming Foundation.