One in Twenty workers in the United States are in the country illegally (about 12 million). Republican and Democratic Administrations have addressed the problem. Traditionally, there is a school of thought that allowing some illegal immigration from Mexico would help bring stability to the Mexican economy and would allow people fed up with Mexico a place to go rather than remaining home, stirring up a revolution (a safety valve).
The US Economy requires some low skilled/no skilled workers but there is no effective temporary worker program to allow the legal access to the US that would address more or less everyone's concerns. The US Congress needs to craft a legal alternative to illegal immigration. A temporary (guest worker) visa plan needs to have sufficient infrastructure to allow about half a million visa per year. The visas must allow workers the flexibility to change jobs so they can move to areas where the demand is high.
Any path to legalization of those in the work force should not be amnesty. The path must include payment of back taxes and security checks of the sort proposed by the US Senate in 2006.
The adequate flow of legal guest workers would drive out illegal workers and would eliminate the need for the present unwieldy employment verification systems.