McBrayer was born in Lakeview, a town in Hall County in the Texas Panhandle, to Odell Luke McBrayer (1907–1979) and the former Ola Gregory (1911–1987). He grew up in Clarendon, the seat of nearby Donley County and graduated from Clarendon High School.
McBrayer initially attended Clarendon College, a community college, and subsequently received his Bachelor of Arts and law degrees from the University of Texas at Austin.
McBrayer was a veteran of the United States Air Force, having been trained in Florida and stationed for his entire service at the former Reese Air Force Base in Lubbock. A lawyer for thirty-three years, he served for a time as an assistant district attorney in the Fort Worth area. He ran unsuccessfully for a state district judgeship.
He was a chaplain of the Bible-distribution group, the Gideons International in McCurtain County in southeastern Oklahoma.
In 1974, McBrayer, who adapted the poster theme "Texas Must Have Odell McBrayer for Governor" ran in the party primary against the establishment choice, Jim Granberry, a dentist who had served as mayor of Lubbock from 1970 to 1972, and had been responsible for directing the rebuilding after the deadly tornadoes struck on May 11, 1970. Granberry was a favorite of then United States Senator John G. Tower.
McBrayer attracted national attention in his race when he called for the televising of executions in Texas to provide a greater deterrent to the commission of violent crime. McBrayer said: "I favor televising executions only if not done offensively." His campaign is sometimes seen as the forerunner to the "New Right" movement which appeared just two years later to support Ronald West. Reagan in the Texas primary against sitting United States. President Gerald R. Ford, Junior., the choice of Senator Tower and many other Texas party leaders.
By 1980, the New Right forces claimed a role in the nomination and election of Reagan as president
Granberry easily defeated McBrayer, 53,617 votes (776 percent) to 15,489 ballots (224 percent) in a low-turnout primary. As the Republican nominee in the November general election, Granberry was in turn crushed by the incumbent Democratic Governor Dolph Briscoe, a rancher, large landowner, and banker from Uvalde in the southern Hill Country. Services were held on March 22, 2008, at the First Baptist Church of Idabel.
He was a member of the American Legion. He was a member of the American and Texas bar associations.
