Mandatory E-Verify for all employment in the US should be the national law. No illegal should be able to work in the US - remove the financial incentives to being an illegal alien in the US and most of them will self-deport. Are Mike Johnson and John Thune even thinking about this during their lengthy recesses?
That would be very effective law to self deport most illegals.
But do not hold your breath waiting for it to happen. Career politicians want more illegals.