To picture how this works, think about the grocery bagger in the supermarket, a classic low-wage service job. Supermarkets hire grocery baggers for the minimum wage, or close to it, because it's a perk that makes their customers' experience a bit nicer and helps move the lines along, possibly requiring fewer cashiers, who cost more to hire than grocery baggers.
Now, if you pass a law saying everyone, including grocery baggers, has to be paid $10 an hour, what happens? The supermarket probably hires fewer baggers, or has them work fewer hours. Perhaps they decide they only need baggers between 4 p.m. and 7 p.m. If you put the minimum wage up to $20 an hour, shoppers bag their own groceries. This is so clear that it's taken some time for the defenders of an ever-rising minimum wage to come up with an adequate theory to obscure it.
The Wall Street Journal condemns minimum wage hikes as economically harmful. It's a pretty trivial conclusion: Any time you distort economic behavior (whether you're a government imposing regulations, or a private individual imposing externalities), you prevent people from acting in a way that's economically beneficial. What's weird is that it's turned into a populist talking point that a higher minimum wage helps poor workers. Maybe reframing the argument would be effective. Instead of a 'minimum wage', call it something like "The Poverty Penalty": If you can't earn what we say you ought to earn, you're not allowed to work at all.
My political opinions are usually pretty nebulously pro-market and anti-interference, which doesn't lead to many serious policy suggestions besides "Don't do it!" But there is one law I think would be pretty beneficial: If a bill is passed by a majority, the minority party gets to pick the name. Whatever your political opinions, you've got to admit that this would make political discource 1) More honest, and 2) More fun.