Answer:
Economics
If Texas decided to secede and become a new nation, I believe they won't face any problem in terms of their economic identity. Vast majority of Texans prefers a mixed economy where they implement Capitalist characteristics with some form of government assistance.
Government
One problem that may arise in Texas when they formed a new nation is determining how much Church influence should exist in Government. The Majority of Texans are religious, so a lot of them might favor Implementing biblically values in their legislations. Some people might not agree with this.
Society or Social Issues
In terms of social issues, Texans generally pretty conservative. Some challenge may arise regarding the existence of LGBT community in Texas as a new nation.