Maynard reached the height of his political career in 1873 when he defeated both Andrew Johnson and popular West Tennessee politician B. F. Cheatham in the race for Tennessee's at-large congressional district. The following year, he ran for Governor of Tennessee as a Republican, but lost to James D. Porter. He was appointed Minister to Turkey and served from 1875 to 1880 in that post. He was appointed United States Postmaster General in the Cabinet of President Rutherford B. Hayes and served from June 2, 1880 to March 5, 1881.