Also, there is reason to believe that higher minimum wages encourage your workforce to become better skilled in order to compete on the world market at their higher price, as is the case in Germany.
Almost need some kind of subsidy somewhere to give these people at least a decent standard of living.
What would stop companies from increasing the costs of their goods and services because they know minimum wage is higher (and people can now afford it)?
Minimum wage in the US is $7.25/hour (many states are higher). A person couldn't support a family on this, but they could find a place to live (either renting a room, cheap apartment, or sharing a bigger apartment with friends) and have enough left over for the bare-minimum.
Contrast that with many right wing arguments about taxation, which usually take the form "Lower/more regressive taxes are always better, and here's why" - disturbingly many of those arguments are "valid" (i.e. if you accept the arguer's claims, the conclusion follows) no matter what the starting point is, and the end result would either be zero taxes for everyone or (surprisingly common) almost 100% taxation of the lower classes and no tax on the upper; hell, if we allow for redistribution, many of the conservative arguments actually imply that the upper class should be given money by the lower class, for the good of the economy.
If your argument pushes some number in one direction but doesn't turn around for some value of that number, then there's typically a problem with the argument; here, that's not the case, the poster explicitly provided that stopping point.