Worth noting that some provisions that hold employers accountable are already law:
(4.) An employment verification system shall be created for employers to verify the work authorization of new hires based on taxpayer identification numbers for citizens, permanent residents, and immigrants on visas.
(a)) Once the verification system is in place, it shall be prohibited to knowingly hire unauthorized workers.
(b)) Employers found in violation of Section 4 - 4a will be assessed a $10,000 fee per violation.
https://uselectionatlas.org/AFEWIKI/index.php/Come_Out_of_the_Shadows_Act
Of course, your bill goes further which raises the fundamental question of how much accountability is good enough. Do we know how well the present law is working? I recall seeing something about this from the GM department a while back but I couldn't dig it up.
This was the report I did back in March, as requested by Yankee. Didn't provide any data on e-verify though.
https://uselectionatlas.org/FORUM/index.php?topic=308863.msg6700442#msg6700442