Now the truth is that raising the min. wage either has no effect or a devastating effect. If the min. wage is below the prevailing wage, it has no effect. If the government imposes a minimum price on BMW's of $10000, it won't make a difference.
If it is above the prevailing wage, the resulting surplus of labor may be small. I.e., just a few schlubs will be laid off. Might be better in the long run, I prefer the automatic checkout to having to talk to the person manning the cash register.
But the big deal here, that everyone now knows, is the cost of union labor. Union contracts are tied to the minimum wage. An automatic raise without negotiation. Whom will this effect? Mostly, it will effect government. Most union labor is either in government directly or works as government contractors. As far as state governments go, this is roads and bridges.
Watch Ohio. They put in a COLA increase for the minimum wage. Disaster awaits them. First, the Democrats will not be able to run on the minimum wage again. They return to it like a dog to vomit. It's their only populist issue. If they cannot agitate for an increase, they have no sure issue to run on. Furthermore, Democrat governors will be handcuffed. They'll find labor eating more and more of the state budget. The state salaries will go up, costs for projects will go up, everything will go up. Either they will have to raise taxes constantly or they will have to do some union-busting.
It will be a beautiful disaster.
You're right, of course, if the new minimum is below the market wage, there won't be an impact. If that's the case, why bother? You're also right about union wages often being tied to the minimum, but I don't think that's as prevalent now as it used to be.
As to Ohio...what is it there with those people? When Celeste was govenor, he passed a bill that required any company that closed their doors to pay an "exit tax" equal to one-half of their annual payroll. (This was when so many companies were fleeing to the south.) Six months later, he was scratching his head saying: "Gee, I wonder why the number of new businesses being formed in Ohio has gone to zero?" Well, duh... At least they were smart enough to strike it from the books.