Williams began his run for Governor of Texas as one of several Republicans looking to succeed outgoing Governor Bill Clements, who had been elected to a second, non-consecutive term in the 1986 election (he had previously been elected in 1978). Clements elected not to run for a third term after he was strongly implicated in a pay-for-play scandal at Southern Methodist University, where he had served as the Director of the Board of Governors in between his terms as Governor of Texas.