Poor people are already coming to the US for economic reasons. The new violence-driven exodus is and will continue to be disproportionately populated by wealthy and well-educated Mexicans. Already they are contributing to the boom in San Antonio, aka Monterrey Norte. They may be refugees, but don't conjure up images of the typical refugees from Haiti or war-torn Africa. Far from it.
The drug-related violence is tragic, reprehensible, and ominous. But it is also overstated and sensationalized. Far more people are victims of homicide in the US annually than are victims of drug violence in Mexico, even when adjusted for population. The violence is isolated to a few states and affects to a large extent only those who are involved in the drug trade. The fighting is proprietary in nature--that is, cartels fight amongst one another for key supply hubs and routes and amongst themselves when their leaders are arrested or killed. Many innocent bystanders have fallen victim in the crossfire, but the vast majority of deaths are of cartel employees and their gang henchmen.
And for what?
So that a few drug entrepreneurs can profit off the insatiable desire for drugs in the US which are sold at ridiculously high prices in the black market.
If we want to avoid a further exodus of Mexicans, wealthy or otherwise, into the US, there is only one solution: legalize it already, dammit. Prohibition always leads to black markets and organized crime. This is no different, except that the organizing and violence is occurring south of the border. We import the drugs and export the dollars and the violence. When the market for over-priced drugs disappears, so will the violence, and so will the additional motive for Mexicans who are understandably following a route to safety.