As a child growing up in Texas, back in the 1970's I can remember the secessionist spouting off about how horrible the Union was treating Texas. I was not real sure what their gripe was or is now. It is unfocused, and seems to be about their feelings when Democrats get into power. I think it reminds them of Reconstruction or something. They just hate loosing so much that they are going to take their ball and go home.
A quick search on the internet doesn't really turn up an actual political party espousing splitting from the Union. There is the Texas and Southern Independence Party that wants to re-establish the Confederate States, but this wouldn't work for Texas. They really don't like or trust Oklahoma. OU recruits too many of the good football players. But there is the Texas Republican Party. Although dissolving the Union doesn't show up in their party platform, which is a scary document. The whole Texas Republican website is scary to me with stuff like this:
I did not know we were supposed to use the Bible to rate our political party. I mistakenly thought that was what the Constitution was for. My mistake.
I hate to brag AGAIN about Alaska kicking Texas' butt again, but Alaska has Texas beat in this area too. We have the Alaska Independence Party. Our governor's husband was a member once. There are also rumors that she is a AIP "Manchurian Candidate." I can't wait for that episode of the Wasilla Hillbillies. The party is libertarian, with reservations. Like we want roads and keep that Permanent Fund money coming but privatize everything else. They are always are around during the elections both when Republicans are in office as well as Democrats. They definitely get points for perseverance.