Ummm no. Texas would not be able to sustain itself. There isn't as much oil wealth as there used to be. Most of the wealth in Texas is now from banking and industry, and all the companies that are headquartered in Texas would probably leave.
People want to live and work here and companies want to be headquartered here because of the lack of an income tax for their employees and a favorable corporate tax rate. This would quickly change if Texas were to secede. It's very different to be a populist state in a larger country and a country unto oneself.
Many of Texas' industries are buoyed by federal money. Lockheed Martin and Bell Helicopter in Fort Worth would lose federal contracts. Sikorsky Helicopters has a large presence in Corpus Christi.
There is also the annoying little issue of Fort Hood. The largest US Army base in the world is in Texas. Over 50,000 US Army soldiers smack in the middle of the state. Add to that six Air Force bases, three other Army bases, a joint reserve base and you can put a soldier on every street corner.
There is still oil here, but it no longer leads the economy, and a lot of what does drive the Texas economy is multinational corporations. A separate Texas wouldn't be nearly as attractive to them as a state of Texas is.
In 1869, Texas v White determined that the union "was as complete, as perpetual, and as indissoluble as the union between the original States. There was no place for reconsideration or revocation, except through revolution or through consent of the States."
Secession talk is stupid. It's the last bastion of the idiot. There isn't a single state in the US that could support itself as a country, and it would take all of a day for the Army to move in and take over.