I sympathize with those on the right thinking this is good in terms of immigration problems, but the e-verify program (even if never abused) is a huge pain for actual businesses to administer and is setup in such a way to open companies up to various legal/discrimination claims.

It is not just a simple put the info in -> green light or red light. It is an administrative pain and a process filled with easy trip wires that permit EEOC and other lawsuits. For small/mid size companies it is especially a net negative risk/return even if they agree that they dont want to hire illegal immigrants.