Skubitz served as administrative assistant to U.S. Senator Clyde M. Reed from 1939 to 1949, and to U.S. Senator Andrew F. Schoeppel from 1949 to 1962. He served as a delegate to the Republican National Convention in 1960.
He was elected as a Republican to the Eighty-eighth through the Ninety-fifth Congresses and served from January 3, 1963, until his resignation December 31, 1978. He did not seek renomination in 1978.
Skubitz died in Wichita, Sedgwick County, Kansas, on September 11, 2000. He was interred at Old Mission Cemetery, Wichita, Kansas.