To verify illegals, green cards, students/tourists who are here legally but are illegals if they work, and citizens ... to verify all of this, the natural tendency will be to check the many other government and commercial databases.
That leads to one big database. I work on some of these databases. Inevitably the government has all the info on you. Due to database errors, maybe 1% of the people will be mis-identified. That means 1% of illegals get jobs ... and 1% of citizens or maybe 1 million are blocked from getting jobs. If they can improve the database to 0.5% then that is maybe only 500,000 citizens blocked from getting jobs. No government database is anywhere close to that accurate right now.
Every call for increasing the accuracy of the database is a call for ever more intrusive government accounting of your personal life.
Then consider, we often flip between an Obama and a Trump, back and forth. What is to prevent the next Obama from adding to the rejection list, fir domestic violence people who used a gun, then eventually anyone on the gun list... because they present danger in the workplace.
e-verify is the spring board for every snowflake fantasy.
That is true.
However, Visa, MasterCard, American Express, Discover seem to have solved this problem. They identify their cardmembers in a second or two over the internet and facilitate payment, no problemo! These capitalists face the same problem (knowing the customer), yet make money hand over fist!
Properly implemented, e-Verify can solve the problem of discriminating between Real Americans, US persons, and los ilegales!