This is what the constituion says. [link] "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."
Basicly, you'd need the OK form both the Texas Government, and Federal Government.
Portions of a state seceding from their parent state has happened twice in our nations history. In the midst of the civil war, West Virginia Seceded from Virginia, the consent of virginia was not needed because they were in revolt, and it got rubber stamped.
At the dawn of our nation's history, Maine Seceded from Massachusetts, this was at the very beginning of the slavery issue, and It scored another free state, and mass was happy to be free of the maine-tards.
That said, no one in any government is planning on seceding any state at this time. I seriously doubt that the majority of people in those states seriously want this. 25,000 signatures is nothing in states with more than 1 million people. Given the amount of signatures are in the tens of thousands, its unlikely that you'd even get someone elected to state government with those numbers.
And yes, people get butthurt every election. They make all kinds of crazy remarks, every election. Most of them are just that, butthurt, and empty gestures that can be safely ignored.
That said, given the continual cultural diffrences between austin and the rest of Texas, I'd say that and East Texas state might not be such a bad thing.
Upstate NY wants to be free of NYC and Long Island, because they feel the state government is dominated by urban and suburban areas is not responsive to the needs of the bulk of area of NY which is farmland.
One cannot stress enough that a petition is just a letter signed by a lot of people. The most that can ever happen if enough signatures are received is that someone in government may be required to read it. Neither petition was created or endorsed by the state or city government, and there is no guarantee that the signatories are texans, Americans or even just actually real people. Discussing them as if they had any more importance than your average forum thread is a waste of time.