Russell approaches the argument with a naive supply-and-demand response, and asserts "This isn't Economics 101, it's Economics 001." Yet in doing so, he's ignoring the core of the more subtle point about the functioning of a monopsony. Essentially, since as an employer, your competitors are also facing higher wages costs, almost all of you can afford to pay the higher rate. Yes, this means that prices go up, but this is indeed equivalent to (roughly) a sales tax, with minimal overhead costs, as Brad DeLong points out.
Certainly supply and demand curves aren't going away, but your classic supply and demand curve is a steep one, as a result of severe competition. The minimum wage, by cartelising the workforce eliminates this competition, resulting in a much more gentle supply and demand curve, the result of which is that you can do a lot of redistribution of wealth for a small cost in employment. The psychological trick employed here is to imply that the severe rigours of the market also apply to the labour market, when in fact, taken in aggegate, the market is far less rigourous: a classical economist's intuition is honed by considering the supply and demand curves experience by a single firm in a competitive market for a particular good.
Tyler Cowen is playing the same trick, in effect, by claiming that employers will cut costs elsewhere, "Gordon notes that the government can make an employer raise nominal money wages, but can't stop him from turning off the air conditioner." This is in fact emotion masquerading as logical argument. An employer is going to want value for money; they wouldn't indiscriminately adjust costs to the "correct rate", for they are going to want an efficient and motivated workforce. Quite possibly, the reverse effect could occur: the workforce costs that much more, so it's more important to keep them efficient, so that you turn the air conditioning on sooner.
The flaw here appears to be the result of imagining that there is a "correct rate", but in truth, the rate is emergent from supply and demand; it is not divinely discovered by an invisible hand doling out "true justice". Employers will spend more or less on the workplace in accordance to how this effects their profits, not (just) their overheads. An investment that paid off beforehand is still likely to pay off. There is little existing slack in the system before the pay rise, since the "extras" not prescribed by law are susceptable to competition, and therefore, if they could be trimmed to save costs, would have been trimmed already.
Update: The Angry Economist has posted a "rebuttal".
My terse response is that it would be moral to have as full an employment as possible if there were no fallback. As there are benefits paid to the unemployed, it's simply not the case that we're sending people into severe poverty if they don't get a job, so the best policy is not maximal employment at all costs.
I expect that he would be opposed to "artificial" job creation, even if it could work, so I think that this is fake emotion. Maybe I'm wrong.