Back when I could get away with logical thinking in my college classroom, when the issue of population control came up, I would ask my student whether the US was overpopulated or underpopulated. They would always respond that it was overpopulated. I would then point out that if every American, all 320,000,000 of them, were moved to a personal half-acre portion of Texas (i.e., two acres for a family of four), there would still be some Texas left over (about 20,000,000 acres, give or take), and the other 56 states (/s) would be, not underpopulated, but unpopulated.
To be more practical, if Texas were to secede and establish itself as a nation based solely on the U.S. Constitution and its first ten amendments--with only those changes such as removing the postal service and the references to allowing slavery--it could easily sustain a population 2 or 3 times its present size of 27 million.
The difficulty would be the extent to which Texas could be self-sustaining: it would have to import a number of necessities such as uranium (and probably oil), and a number of desirabilities such as, say, oranges or bananas. But economics makes for strange bedfellows, and the socialist dictators of Calimexico would figure out ways to sell Texans oranges.
The main issue is the same one that existed in 1861. If the full force of the US military were put into use to overturn the secession, the combined forces available in Texas would not be able to overcome it--the result might be a nuclear wasteland, but there aren't enough arms to turn back a US military onslaught. In order for the Texas secession to succeed, the split would have to be, if not amicable, at least not hostile.
If Texas goes, it would probably take a few other states with it.
“...the result might be a nuclear wasteland”
If this ever came to be, I can guarantee you that Washington DC would cease to exist, along with its 100 mile radius of suburbs.