Branigin was a conservative Democrat who oversaw repeal of the state's personal property taxes on household goods, increased access to higher education, and began construction of Indiana's deep-water port at Burns Harbor on Lake Michigan.

In 1968 Branigin received national attention when he ran as a stand-in for Lyndon B. Johnson in Indiana's Democratic presidential primary.

Johnson dropped out of the race on March 31, 1968, but Branigin continued to run as a favorite son candidate against Robert F. Kennedy and Eugene McCarthy.

[2] In 1930 Branigin took a job as attorney for the Federal Land Bank and the Farm Credit Administration in Louisville, Kentucky.

After Democratic gubernatorial candidate Henry F. Schricker won the election that year, he appointed Branigin as chairman of the state conservation commission.

Branigin's Republican opponent, incumbent Lieutenant Governor Richard O. Ristine, had cast a tie-breaking vote in the Indiana Senate allowing a state sales tax, which was an unpopular decision among voters.

During Branigin's term as governor, he also oversaw the repeal of the personal property tax and began work on the Port of Indiana, the state's first deep-water harbor on Lake Michigan.

[6] In early March 1968, President Lyndon Johnson asked Branigin to run as his stand-in during the Indiana Democratic presidential primary.

When Johnson announced he would drop out of the race on March 31, Branigin decided to continue his campaign, hoping to control the state's votes at the Democratic convention in Chicago later that summer.

In later years he served as president of the Greater Lafayette Chamber of Commerce, the Harrison Trails Council of the Boy Scouts of America, and a board member of Franklin College and Purdue University.