Big business? Sure, a little bit.
Republicans? Oh yeah, they definitely get some blame.
Ted Kennedy? Hell yes.
Democrats? Of course.
The mexican government? Well yes, they are partly responsible for using our borders states as a relief valve for social and political pressure.
The immigrants themselves? A little bit I guess. Remember that they are simply responding to economic incentives.
How about the farm lobby? Probably not but you should rest a lot of blame on them. I hold firm to the notion that they are more responsible for the illegal immigration situation than any other group or politician in the country.
One of the things the farm lobby in this, and many countries, has done is to lobby for ridiculous subsidies and it has been wildly successful in doing so. As a result of those subsidies, farm innovation has diminished as the competitive environment has been corrupted by said subsidies. One of the results of this is that farming technology has grown very stale (with most growth coming by way of biotech) leaving very few ways in which to increase yields or lower costs in an environment of growing labor costs. So what they did instead was simply import people who would be willing to work well under market value doing work that should be done by machines. Machines which weren't invented or put into use because the farm lobby was able to use the government to provide them with artificially cheap labor.
This is just another one of the many problems brought about by America's most powerful lobby.