We've discussed a minimum wage in the past (see here and here), and I think i'm right in saying that both sides acknowledge the economic logic that a miniumum wage, ceteris parabus, increases unemployment (especially amongst low-skilled workers).
You might believe that the labour market is fairly inflexible, and that the firms can absorb the rise in costs to imply that in practice a minimum wage merely creates a slight reduction in expansion (and no new unemployment) coupled with mild inflation. It's an intuitive belief, but try claiming it with a straight face in light of this.
In short, I don't think there's enough employment opportunities for young, non-white, low-skilled workers, and therefore miniumum wage laws are inherently wrong. They protect the relatively well off at the expense of the relatively worse off.
I also think both sides in the debate accept that minimum wage laws were founded on sexist and racist principles: the progressives knew full well what the effects were. Their policy wasn't based on ignorance, but on eugenics.
Nowadays though advocates of a minimum wage are left in a difficult position. They support something which they know is harmful (they don't doubt the economic theory), and something that they know is grounded in eugenics (they don't doubt the economic history). So how can one support a minimum wage without either being ignorant or an advocate of eugenics? (That question isn't rhetorical by the way..)
Alex Tabarrok points out a horrific NYT op-ed that acknowledges that an economically literate non-racist can't support minimum wages. The cloak comes off and they declare themselves as racist and nationalist:
If we are really serious about turning back the tide of illegal immigration, we should start by raising the minimum wage from $5.15 per hour to something closer to $8.
If we raise the minimum wage, it’s possible some low-end jobs may be lost; but more Americans would also be willing to work in such jobs, thereby denying them to people who aren’t supposed to be here in the first place.
In other words, because a minimum wage hurts foreigners even more than Americans, it should be adopted. The policy harms immigrants, and also harms low-skilled (typically African-American) US workers, but because relatively high-skilled (typically White) US workers benefit it's deemed good.
It's refreshing for minimum wage advocates to cut out the rhetorical bullshit about wanting to help the poor, and actually admit that it's a policy for racists and nationalists, and the uninformed. For such vocal supporters of a minimum wage to say "Yes, we accept it's a racist policy and that's why we like it", should, hopefully, further undermine a policy that may not create much economic damage, but certainly is symptomatic of how faulty economic reasoning can persist.