A lot of what we're seeing now are Central Americans fleeing massive violence in places like Honduras due to the drug trade shifting around, not solely economic migrants.
If the US wants to resolve the immigration issue long term it needs to fix visa overstays and stabilize Mexico/Central America by ending the drug war plus providing economic assistance.
While I wholeheartedly agree with you about ending the drug war the stats that I have seen on Central American illegals doesn't show them as a significant portion of our current illegal population, yet. Regardless, if you cut off their ability to work and their access to public funds then what good does it really do them to be an illegal here versus an illegal in a South American country that they can find work in?
I may be naive but visa overstays should be something that is relatively easy to handle in the broader scope of the issue.