Both Brad DeLong and Steven Landesburg get the minimum wage argument wrong (thanks to Tyler Cowen for pointing me to them. Don Bordreaux has also blogged on it recently.). The theory predicts that a minimum wage will destroy jobs. You sell the most of something when you're free to set your own price. If somebody forces you to set it higher or lower, you'll sell less or more than you would like. If somebody forces you to sell your labor for a higher price than you'd like, you'll sell less of your labor. This isn't Economics 101, it's Economics 001. If it's not true, all economists go home and cry into our beer because our work is all completely wrong. In order to arrive at a conclusion that goes against the theory, you need very good empirical data. If you want to prove that light can travel faster than the speed of light, you need very good evidence. That data doesn't exist.
The data is in fact crummy given the size of the increases in the minimum wage. First, the minimum wage intentionally affects very few workers. Second, the minimum wage is only increased after it isn't really necessary. Third, you can count the people who got more money, but you can't count the people who lost their jobs.
I took a course in statistics when I worked in production engineering at Hewlett-Packard. They emphasized several points. In order to get good data, you can't just monitor your processes. You have to run experiments at the limits of your processes. You have to replicate to reduce experimental error. You have to randomize to eliminate changes over time.
So, in order to answer the minimum wage question, you can't just increase the minimum wage by a few cents and then go measure everything you possibly can measure. You have to both completely eliminate it, and double it. You have to do it for two randomly-selected populations. Nobody wants to run that experiment. Everybody knows what would happen if the minimum wage was doubled: Huge numbers of people would lose their jobs. That's exactly what happened in Haiti in the 1930's when a continental US minimum wage law accidentally applied to Haiti. So, really, everybody who refuses to run the experiment has the answer firmly in their head; it's just in their heart that they refuse to acknowledge it.