Thirty-one percent (31%) of Texas voters say that their state has the right to secede from the United States and form an independent country.
However, the latest Rasmussen Reports poll in the state finds that if the matter was put to a vote, it wouldn’t even be close. Three-fourths (75%) of Lone Star State voters would opt to remain in the United States. Only 18% would vote to secede, and seven percent (7%) are not sure what they'd choose.
Texas rejected a treaty of annexation. Bringing Texas into the United States was accomplished by a Joint Resolution of the US Congress, and an Ordinance of a special convention in Texas. Neither the US Joint Resolution, nor the Texas Ordinance, address the issue of secession at all. Texas did reserve the apparent right to divide itself into other states, which has been proposed at various times, and which would today probably produce a bunch more Republican Senators, and possibly a couple of Democrats.
The 1866 Ordinance is really no impediment to secession either, since a further convention could simply repeal this Ordinance also -- just as the 1861 convention repealed the Ordinance of Annexation. Probably none of this will ever happen, but the right of the people of a state to resort to secession is implicit in the entire concept of republican institutions, ordered liberty, and self-government. Whether secession can be successful is more a question of popular will and raw power than it is of law.