Thatcher worked in farming, on a newspaper and in county offices. He was elected Butler County, Kentucky circuit court clerk in 1892 and served from January 1, 1893, until his resignation in 1896. He studied law in Frankfort, Kentucky and was admitted to the bar in 1898, commencing his law practice in Frankfort. Thatcher was an Assistant Attorney General of Kentucky 1898-1900 and then moved to Louisville, Kentucky in 1900. He was an Assistant United States Attorney for the Western District of Kentucky from 1901 to 1906 and a state inspector and examiner for Kentucky 1908-1910.

Thatcher was also a member of the Isthmian Canal Commission and civil governor of the Canal Zone from 1910 to 1913. Thatcher was the Commission's longest-lived and last surviving member.

During his congressional tenure, he guided the passage of several Kentucky landmarks and parks: Mammoth Cave National Park, Lincoln's birthplace, and the Zachary Taylor National Cemetery. He gave up the Republican nomination in 1932 to retain his House seat in order to run for the Senate, which he lost.

Thatcher served on the general counsel of the Gorgas Memorial Institute of Tropical and Preventative Medicine, Inc., Washington, D.C. beginning in 1939 and became vice president in 1948, a post which he held until 1969 when he was made honorary president, a position only previously reserved for Presidents of the United States.

As`of 2006, he was the longest-lived person to have served in the United States Congress.