Absolutely! Been saying this for years - and you are also right: neither party wants it. You are wrong, however, when you say it will never pass. It has been established law for a long time as far as I know. I wish Trump would enforce it.
Perhaps the GOP has told him they will not fight impeachment of he does enforce E-verify. What a simple non-violent solution E-verify would be!
The problem is that it is voluntary not mandatory. Which means that only the companies that have no intention or need to violate the law are the ones participating in the program.
Its a complete joke and congress designed it that way.