Born in Anniston, Alabama, Jeffers attended the public schools and the Alabama Presbyterian College at Anniston.
He served with the Alabama National Guard from 1904 to 1914. He served as clerk of the circuit court of Calhoun County, taking office in January 1917. He resigned that office in May 1917 and entered the United States. Army, serving with the Eighty-second Division in France.
He was awarded the by the United States Government.
He was promoted to rank of major of infantry. Jeffers was elected as a Democrat to the Sixty-seventh Congress to fill the vacancy caused by the death of Fred L. Blackmon.
He was reelected to the Sixty-eighth and to the five succeeding Congresses and served from June 7, 1921, to January 3, 1935. He served as chairman of the Committee on Civil Service (Seventy-second and Seventy-third Congresses).
He was an unsuccessful candidate for renomination in 1934.
Resided in Daytona Beach, Florida, until his death there on June 1, 1983. He was interred at Arlington National Cemetery.
Member, Alabama N.G., advancing to Captain, 1904-1914. Captain, Infantry., United States Army, 1917. Assigned to command Company C., 326 Infantry., 82 Division.
Served in France, at St. Mihiel and Meuse-Argonne. Twice wounded. Awarded Distinguished Service Cross. Promoted to Major; honorary discharged July 1919.
Democrat Member; American Legion. Masons. Club: Civitan (Anniston, Alabama).
Spouse Martha Ruth Burton, November 1, 1911.