What good does it do to arrest these "immigrants"? If they ever do get deported, they are usually back across the border before the ink even dries on the deportation order. Now, if we could deport them to somewhere like Tierra del Fuego, or Antarctica, it might be worth the bother.
Short of that, the best solution is to make sure they don't get here in the first place.
A wall doesn't necessarily mean the Great Wall of China, something like a three tiered fence with the middle fence being energized would work wonders.
Tunnels? In oil country (which much of Texas is) they use vehicles that "pound" the ground, making small earth quakes that enable them to "see" oil bearing strata by using Richter scale readings. Going along the border with these machines would collapse the tunnels while they were being dug. Lose a few guys, and they will decide it's not worth it.
Along with those solutions, cut off the welfare spigot to illegal aliens, fine those who hire illegals $10,000.00 a day per person, no drivers license for illegals, no more "anchor" babies. Take away the reasons for them to come here, and they will decide to go somewhere else.
All those countries who denounce us for not wanting to take these people in can put their money where their mouth is...they can take them. Let's see how long that will last.
We have more than enough population here as it is, and the "politically correct" way that the country has been run the last few years has made it difficult to even take care of them (20 trillion dollars in debt? How freaking ridiculous). We can no longer afford to take in the "Huddled Masses", and the people of this country need to come to that realization while we still HAVE a country.