Stubblefield was born and schooled in Kentucky and attended the University of Arizona for one year in 1927.

Stubblefield served as a lieutenant in the United States Navy during World War II.

Stubblefield defeated the incumbent Congressman Noble Jones Gregory in the Democratic primary and won the seat in the general election.

After winning the election Stubblefield resigned from the Railroad Commission on December 31, 1958, in preparation for his service in Congress.

Stubblefield unsuccessfully sought re-election to his House seat in 1974 but lost in the Democratic primary to state senator Carroll Hubbard who went on to win the general election.