At the age of twenty-three, Parmer served as the youngest legislator in the Texas House of Representatives for a single term from 1963 to 1965. Thereafter, he was elected to the Fort Worth City Council in 1975 and became mayor of Fort Worth in 1977, a post he held for two years until his defeat in 1979 in a heated contest with Woodie Woods. Parmer was then elected as a state senator in 1982, where he defeated Andy Andujar, the husband of State Senator Betty Andujar, the first Republican woman to serve in the state Senate. Parmer served on the Senate committees of State Affairs, Health and Human Resources, Chairman of Intergovernmental Relations, Chaired the Special Senate Committee on Hunger in Texas in 1985, and Chair of Democratic Caucus of Senate in 1987. In 1989, Parmer was one of five senators to serve as the President Pro Tempore, having preceded in that position his regional colleague, Bob McFarland of Arlington. In 1988, at the age of forty-nine, Parmer was admitted to the practice of law in Texas. He took and passed the State Bar Exam without attending law school under an old state law permitting the substitution of years of legislative service for law school hours. From 1991 to 1998, Parmer was the managing shareholder of the law firm Parmer, Archer, Young and Steen. Parmer ran two unsuccessful campaigns for the United States House of Representatives and one for the United States Senate. In 1984, as a freshman state senator, he lost the Democratic nomination in District 6 to former State Representative Dan Kubiak of Rockdale. Kubiak was then defeated by Republican Joe Barton, who held the seat until 2019. Barton succeeded the Democrat-turned-Republican Phil Gramm, who was first elected to the U.S. Senate that year over fellow Republicans Ron Paul and Henry C. Grover and the Democratic State Senator Lloyd Doggett of Austin. In the U.S. Senate race in 1990, Parmer polled 1,429,986 votes, but Gramm prevailed, 2,302,357. In 1996, as the Democratic nominee in District 12, Parmer polled 41 percent of the vote against the Republican Kay Granger, also a former mayor of Fort Worth.
Humanitarian career
In 1998 Parmer was appointed by U.S.President Bill Clinton as the Assistant Administrator of the U. S. Agency for International Development in charge of the Bureau of Humanitarian Response. Parmer was unanimously confirmed for the post by the Republican controlled U. S. Senate. During his tenure at USAID, Parmer was largely responsible for U.S. humanitarian operations during the Kosovo War. After the election of President George W. Bush in 2000, Parmer was selected as president of the American Refugee Committee, an international humanitarian relief organization with programs in 14 conflict impacted countries around the world. In 2008, he was elected to the board of directors of Interaction, the largest association of U.S. based private relief and development organizations.