Final answer:
In 1990, the Texas Republican Party faced a significant setback when Democrat Ann Richards was elected as the governor of Texas, indicating a shift in the state's political alignment at the time.
Step-by-step explanation:
The Texas Republican Party suffered a big setback in 1990 when Democrat Ann Richards was elected to the governor's office. This event marked a significant political shift in Texas, as Republicans had previously maintained a strong hold on the state's executive leadership. The election of a Democratic governor demonstrated the evolving political landscape of Texas during that period. Throughout the 1990s, Texas would see further political developments, leading to the eventual dominance of the Republican Party in statewide elections towards the end of the decade and into the new millennium.