From the “Texas Secede” web-site:
Q: Doesn’t the Texas Constitution reserve the right of Texas to secede?
A: This heavily popularized bit of Texas folklore finds no corroboration where it counts: No such provision is found in the current Texas Constitution[1] (adopted in 1876) or the terms of annexation.[2] However, it does state (in Article 1, Section 1) that “Texas is a free and independent State, subject only to the Constitution of the United States...” (note that it does not state “...subject to the President of the United States...” or “...subject to the Congress of the United States...” or “...subject to the collective will of one or more of the other States...”)
Neither the Texas Constitution, nor the Constitution of the united States, explicitly or implicitly disallows the secession of Texas (or any other “free and independent State”) from the United States. Joining the “Union” was ever and always voluntary, rendering voluntary withdrawal an equally lawful and viable option (regardless of what any self-appointed academic, media, or government “experts”—including Abraham Lincoln himself—may have ever said).
Both the original (1836) and the current (1876) Texas Constitutions also state that “All political power is inherent in the people ... they have at all times the inalienable right to alter their government in such manner as they might think proper.”
It takes 34 states to come together and put a stop to the Federal nonsense.