Most states already have sales taxes;some more onerous than others!
Since ILLEGALS will just go on welfare and/or get paid “under the counter”, raising the minimum wage is dumb. And why wouldn’t they move to where the minimum wage/the welfare payments are higher; which are BLUE states?
I don’t think you really though this through.
If they want to go to blue states with higher welfare payments, then fine, problem solved. I was only trying to keep them out of red border states. (But I would not overestimate blue states "inclusiveness." The democrats are run by the lilly whites, and the lilly whites are segregationists. Lilly whites like minorities in the abstract, somewhere-over-there form, not the put-them-next-door concrete form. Start dumping illegals off in Aspen, CO or Carmel, CA and see how fast this problem gets solved with one phone call.)
Sure, the immigrants would want to go to the states with higher minimum wages. But how many of them are qualified for a $15/hr job? Indians coming for Java jobs are, but not the average day laborer. And there will be fewer jobs available, since those $15/hr minimum wage jobs will be automated away.
Maybe they can work illegally. But they would still pay the sales tax, and it would be a higher cost of living than a state with a low sales tax.
People migrate for economic opportunity. If states don't provide it, they will go somewhere else, to a blue state or even back home. These are things border states can do on their own, no begging the federal government to do anything.