Couldn't they station State Troopers or military at interstates where they cross state lines (like where they have the state "welcome" stations at every state line--at least, they have those here in the south, when we've gone from GA to TN, NC, SC, AL, or FL, so I assume they have those at every state line?).
In theory, it would be possible on the interstates. But on the 100's (or maybe 1000's) of other smaller crossings, that is a massive amount of man power to keep up and running 24-7. Some states where there are mountain ranges, or where there are rivers as borders, that might be possible. But even then it would be a huge manhour investment when there is not enough to go around as it stands.
There are about 78,366 peace officers in Texas. If the average border crossing had 6 officers posted, that would mean that only about 3200 crossings could be staffed if they worked in 8 hour shifts with no days off, and all the criminals decided to stop doing crime, since there were no cops left to arrest them. If they use the military, and they use the all the Army National Guard, Reserves, and Marine Reserves that give about 700k for the whole nation which is about 14,000 per state (but obviously some states need much higher numbers than others). Obviously this whole paragraph of numbers is extreme and not realistic.
I don't know how many crossing there are in most states, or even in Texas, but it seems like setting up meaningful checkpoint would be impossible. On the other hand, checkpoints that are "just for show" on a few well travelled interstates might have political effect.
If anyone has a way to look up the number of crossing from one state to another (without pulling it up and counting), I'd love to know. I couldn't find any info in duckduckgo, but probably looking for the wrong key words.