A (big) decrease in employment would be sufficient to tank the minimum wage, but it ain't necessary. I'd say, concentrating on employment is a bit of a red herring.

A worker's compensation is a whole basket of pay, working conditions, career advancement opportunities, prestige etc. Similarly, what a worker does for the company is a whole basket of things.

Minimum wage outlaws baskets where pay per official hour is under some threshold.

For an illustration of different baskets, have a look at the hectic life and relatively higher pay you get working for Aldi with the more measured pace and lower wages at Walmart.