Greenberg was an analyst at The Heritage Foundation, a writer for the libertarian Cato Institute, and a teacher at the high school and college level in the fields of philosophy, political science, and computer programming. He published over 100 articles on government and public policy in newspapers, magazines, and academic journals, including for The New York Times, National Review, The Monist, and the Ohio State Law Journal. He has been president of the Advance Arkansas Institute, senior counsel for the Center for Class Action Fairness, and chair of Arkansas's Alcoholic Beverage Commission. In 2017, he was appointed senior policy advisor to the Secretary at the U.S. Department of Labor in Washington, D.C.
When he ran for the state legislature in 2006, he was endorsed by the incumbent in the seat, Jeremy Hutchinson, who was prohibited by term limits for running for reelection. Greenberg and Hutchinson had run against each other for the seat in 1999 as primary opponents, an election that Hutchinson won. In May and June 2006, Greenberg placed first in the district's hotly contested primary and runoff and was elected to succeed Hutchinson in the legislative seat for which the two had once competed.
Greenberg served on the Public Transportation and State Agencies committees. He was vice chairman of the State Agencies subcommittee on Constitutional Issues.
Greenberg made national news[6] when he proposed the "Edifice Complex Prevention Act" barring naming public facilities after living people. "In the old days we had a tradition of waiting to judge a person's whole life before we named a building after them," said Greenberg.[6]
After being elected two terms as Arkansas State Representative, Greenberg ran for the District 21 seat in the Arkansas State Senate. He lost to Jeremy Hutchinson in the 2010 Republican primary.