We could save a lot of money and solve a lot of problems if we just eliminated illegal immigration altogether. I know how this can be done. Drop most of our (ineffective) immigration policies!
Let people freely come and go. Some poor guy from Honduras who is just trying to earn enough money to feed his family is not evil. And most independent studies (all that I have ever found, but I am leaving room for mistakes) show that illegal immigrants don't take jobs, they actually boost the economy. A lot of people don't see this, but they are falling into the same trap that liberals do about the economy. It is not a zero sum game. There is not a fixed amount of wealth that has to be divided fairly, like liberals want. And there is not a fixed amount of jobs that need to be hoarded, the way conservatives want.
We would also be safer. The vast majority of immigrants are hard working and honest people. As long as we use prohibition (which never works, see drugs, alcohol, prostitution, gambling) we will have a black market. The problem with black markets is that they are virtually impossible to police, regulate and control. Since we creating a black market on immigration, we are setting up bad things. If everyone who wanted to come, could come, then we could easily funnel them through checkpoints. Why sneak in if you can come through legally and register on your way in? The only filters we use at the checkpoints is for criminals, terrorists, and others of that ilk. That means that the people who do try to sneak in are genuinely bad people that we don't want. As it stands, we can't see the trees (bad people) for the forest (all the other immigrants) in the mass illegal and smuggling that goes on. We can't stop it. Let's use it.
