Imagine the political mess this would cause

From FiveThirtyEight
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From the things you never knew, or at least the things I never knew, department -- when Texas was admitted as a State it was granted the right to subdivide itself into a total of 5 states. If Texas did split, it would lead to 8 new Senators which would wreck havoc with the current partisan balance. 

The Strange Maps article What's the Plural of Texas examines various bouts of "Divide Texas" fever that have struck from time to time, as well as presenting maps of proposed splits.    

However, as entertaining as the thought of Texas multiplying itself is, in reality Texas has no such right. The language about dividing Texas was put in the annexation bill because of the issue of the balance between admitting free state or slave states that so bedeviled America prior to the Civil War. In fact, the only time serious thought was given to Texas dividing was at the admittance of California as a free state. This issue, as well as claims by Texas to parts of Colorado and New Mexico were settled by the Compromise of 1850.

Finally, Texas succeeded from the Union during the Civil War and the terms of their subsequent readmission effectively moot the original annexation act. As a result they're now covered by Article IV, Section 5 of the constitution which reads:

New states may be admitted by the Congress into this union; but no new states shall be formed or erected within the jurisdiction of any other state; nor any state be formed by the junction of two or more states, or parts of states, without the consent of the legislatures of the states concerned as well as of the Congress.

So much for Texas unilaterally dividing itself. None the less, the original terms of Texas' annexation are an interesting quirk of American history and, if nothing else, provide the chance to, from time to time, draw fanciful maps and name new States.