In 1956, he became chief economist and staff director of the Subcommittee on Foreign Trade Policy and the United States House Committee on Ways and Means.
In 1960–61, President-elect of the United States John F. Kennedy named Rashish secretary of his Task Force on Foreign Economic Policy and the Task Force on the Balance of Payments.
From 1967 to 1971, he was a consultant to the United States Congress Joint Economic Committee.
He later served on the presidentially appointed Advisory Committee for Trade Negotiations and was elected chairman in 1980.
Rashish died of lung cancer at Sibley Memorial Hospital in Washington, D.C. on May 22, 1995, at the age of 70.