Final answer:
Texas Republicans have faced setbacks in congressional elections, particularly during economic downturns and midterm elections, exemplified by the loss of control of the House to Democrats in 2018.
Step-by-step explanation:
The Republicans in Texas have experienced setbacks in various elections over time. A significant instance occurred following the congressional elections, specifically during the early 1870s when the United States faced an economic downturn which led to Democrats blaming Republicans for the ensuing economic depression. Furthermore, Republicans have also faced challenges during midterm elections, a notable example being the 2018 election when control of the House returned to the Democratic Party after eight years of Republican control due to the reverse-coattail effect, where the sitting president's party tends to lose seats.