What's the point?
The US population is not going to put up with shooting illegal border crossers or laying minefields or anything fatal.
If the TNG arrests them, then what? There's no where to house them. If you turn them over to the feds, we know how that program works. You could try and turn them around, but Mexico doesn't want them back, and will facilitate them crossing again tomorrow. If they even turn around, short of force.
Is Texas going to finance and build a wall?
Reading the article, the actions he mentions are:
1. activation of National Guard and Texas Department of Public Safety personnel to safeguard the border and turn back would-be migrants from illegally crossing the border. See above. What are they going to do if they don't turn back?
2. DPS personnel will also be order to arrest and return illegal migrants to the border. And then what? incarcerate them? where? Turn them loose in Mexico to cross again?
3. The governor went on to claim he will be deploying gun boats for defense of the southern border and will designate Mexican drug cartels as foreign terrorist organizations. Again, he's not going to be capping drug mules in the Rio Grande. Designating the cartels as terrorist organizations might help, but unless the TNG is going to run search and destroy ops in Mexico I'm not seeing how they can do too much.
I applaud Abbot for wanting to do something in the face of the Fed's complete fecklessness, but I don't really see what he hopes to accomplish. This being 2022 though, and the craziest timeline, maybe the TXANG will drop some JDAMs on Cartel mansions 'ala Clear and Present Danger. That would stir up the *expletive deleted*it but good.