The best thing the government could do is provided visibility into the policies i.e. 'we're going to require $X min wage on this date, and $Y on this date, and after 20XX we're going to be checking on businesses, starting with fines in the first 6 months, and then more serious.
The system would have to adapt - and it absolutely could.
There is some possibility it would happen in that the notion of providing a 'living wage' to everyone would be popular, and it could by virtue of a Supreme Court ruling for example be extended to everyone. It would be then up to the government to theoretically enforce wages and standards for non-citizens, it comes down to the political will - plus - there will be millions pushing for it, thinking about their own personal gain, not necessarily piecing together the likelihood of keeping their jobs. I bet most undocumented workers, once they find out they are legally entitled to a bunch of things, and would have the protection of the justice system ... would push for their ostensible rights.
It would be a pragmatic solution to the 'gaping hole' in the economy, civility, lawlessness and solve a lot of problems at once.
Instead of ICE kicking out illegals, they turn on their head and start enforcing labour laws ... which paradoxically has a much more powerful effect on the border.
But yeah, very unlikely.