Earlier quoted context omitted.
You can look up the debate via the Wikipedia article and other sources. The case for reduced jobs in most situations is very strong, the arguments about overall welfare more intense. Often analytical (rather than emotional) minimum wage proponents admit a small decrease in total employment but think the benefits to those who make the cutoff helps offset that. That might even be true in a growing economy with generall…
Let's say we cut minimum wage in half. How many jobs are going to be created? If it's not profitable for the business to hire a worker at $7 an hour, is it going to be at $3/hour? That's a business with crazy low margins. Pretty much right now minimum wage workers usually do service jobs (fast food, waiting, etc), household chores (cleaning, landscaping), farming, or no-skill manufacturing. No-skill manufacturing is…
There are some people who can only be hired with a wage below the minimum:- high school dropouts, immigrants, physically disabled, blind, mentally ill, elderly, long term unemployed. By setting up a minimum wage too high you are ensuring all these people will not get jobs even if they want or need one. To the employers eyes: if you had to pay $7/hr anyway to hire someone, you might as well hire someone who is physically strong, understands english and has graduated high school.
The minimum wage makes people on the lowest tier unemployable. Arguably it does raise wages for workers on the people near the bottom but not quite there. As you can see there is certainly a trade-off to be made.