A Policy Analysis of [1] E-Verify by the CATO institute concludes that, among other problems, American workers would suffer with wide-spread implementation of the system.

The US needs to reform its immigration system to reform its immigration system in a holistic manner, not piece-meal.  I believe its fair to say that most Americans are somewhere in the middle when it comes to immigration reform.  Enforcement combined with additional visa availability and an opportunity for the undocumented to come out of the shadows and earn a path to legalization is the best way to go.