What this all boils down to is a problem of bargaining power. If you increase the number of workers in a market, but don’t increase the number of jobs proportionally, employers can play workers off one another, driving wages down. That’s why some Republicans like Alabama Sen. Jeff Sessions — whom Walker is apparently taking his cues from — are opposed to increasing legal avenues for high-skill immigrants. Tech workers, doctors, lawyers, and other professionals don’t like seeing their incomes reduced either.

But immigration policy doesn’t occur in a vacuum. There are lots of ways we could increase worker bargaining power, especially for low-skill Americans, while still taking in many more immigrants than we do now.

We could break up the work the economy already provides into smaller chunks that can be distributed to more workers, through things like national paid leave mandates, paid vacation, strengthened overtime laws, and a shortened work week. We could get the Federal Reserve to run much more aggressive monetary stimulus, or even fundamentally reform the way the that policy operates, so that the boost the Fed pumps into the economy goes straight to the Americans hardest hit by bad economic times. We could ramp up government stimulus spending, the generosity of the social safety net, or both, which would also create jobs. And we could change laws to make unions more powerful, so they’d be ready and waiting to take on new immigrants as members and fight on their behalf.