It's amazing that E-Verify was passed in Florida against the massive resistance of the mostly Republican large business interests in Florida. Now the mass-immigration propagandists are already angrily attacking the bill.
It's apparently a very moderate E-Verify: From what I've read, it only applies to businesses with more than 25 employees, and current unauthorized immigrants are grandfathered in. I personally think it should apply to all employers - by now all employers have a laptop and/or cell phone and can check on the legality of any employee in a few minutes. And employees have the right to appeal if they want to. And I believe the employers should be punished, not the immigrants (they have enough problems).
Unfortunately, many Americans believe that all immigrants that want to come here should be allowed in unless they are terrorists or mass murderers, and they view laws constraining immigration as equivalent to the Jim Crow laws. I can assure you, if the people that believe in quasi-open borders take long-term power, the USA will have well over a billion people by 2100. See the government's own projections: https://www2.census.gov/programs-surveys/popproj/tables/2000/2000-national-summary-tables/np-t1.pdf
Remember, no environmental problem in the USA is improved by massively increasing the American population, and immigration is now the primary driver of population growth in the USA.