Sorry, but that has been proven to be totally inadequate as the majority of illegal aliens do NOT work! Yes, enforcement of penalties against employers must be stepped up, minimum $10,000 fine per illegal alien employed made mandatory.
But the biggest draw for most illegal aliens is welfare-types of benefits. Welfare, food stamps/SNAP, WIC, Medicaid (& free emergency room treatment), housing subsidies, and all the rest of the "freebies" & subsidies they obtain from various sources are the #1 draw for illegals. Require proof of US citizenship of any applicant and ALL members of the household to qualify for any sort of benefits.
Also note that most illegal aliens who work "jobs" rather than occasional labor use stolen identities, SSNs, etc. So the conscientious employer who uses e-verify is deceived since such "true-name" identity theft will e-verify! Punish the illegal aliens themselves with conviction of felony identity theft, identity fraud, with mandatory hold until deportation, with permanent bar to reentry. Don't punish only the employer & let the illegal aliens go free. Punish the illegal aliens themselves with detention until deported with permanent bar to reentry as well as the employer's penalties.