I don't disagree with you, but I'd also suggest that illegal immigration by itself is not really the problem. The REAL problem is that illegal immigration -- combined with a bloated welfare state -- is a recipe for financial disaster. There's a reason why California's problems with illegal aliens are orders of magnitude worse than those in Texas. It's because California spent several decades building a welfare state that attracted these aliens like a porch light attracts moths.
Eliminate the welfare state and you eliminate a big chunk of the problem.