There have been dozens of articles in the academic literature on the impact of the minimum wage on employment, particularly on the employment of low-skilled workers. Virtually every one of these articles finds that an increase in the minimum wage reduces employment. As Don points out, this is just one of the negative impacts of the minimum wage. There are other effects that are harder to observe and measure—on the job training, the expected level of effort to be put forth on the job and so on.
Economists have done an immense amount of work trying to measure these effects and the overall impact on the poor. The overwhelming consensus has been that minimum wages serve the poor very poorly. The standard finding is that a 10% increase in the minimum wage reduces employment among low-skilled workers from 1% to 3%.
This consensus was challenged in 1993 in a series of papers by Card and Krueger. Using a very different methodology from previous research, they found virtually no effect on employment and some evidence that an increase in the minimum wage might increase employment among low-skilled workers. Card and Krueger’s work generated a critical response questioning the reliability of their findings.
I do not find the Card and Krueger findings compelling. Some do.
Even if you don’t, you can still think it a good idea to put 1% or 3% of low-skilled workers out of work in return for a 10% increase in the wage of those who keep their jobs. Personally, I find that to be a very unattractive trade-off, especially when you consider the non-employment effects, but that is a judgment call.
There have been many surveys of the literature on the impact of the minimum wage. The only one I could find on the web that is publicly available is this survey from the Joint Economic Committee . Scroll through the bibliography at the bottom. The author has an ax to grind (the author doesn’t like the minimum wage) but it will give you an idea of how much effort has been made to discover the actual impact of the minimum wage. Here is a pro-minimum wage survey  of articles.
None of the articles are casually done. Most or all of them involve a complex set of statistical techniques to try and hold constant the other factors that affect employment. This is hard to do. Reasonable people disagree over when it is done well and when it is not. A pretty persuasive argument can be made that is nearly impossible. (If you have access to JSTOR, you can find John Kenna’s superb article  reviewing of the difficulties.)
A few more thoughts. Politicians like the minimum wage because the cost of financing it is paid by three groups—the workers (in the form of lower employment), employers (in the form of lower profits) and consumers (in the form of higher prices). Missing from that list is taxpayers—so for politicians, if the negative effects are hidden from most voters, the minimum wage is close to a free lunch. So it is preferred by politicians to the earned income tax credit (EITC) which costs tax dollars. Most (all?) economists argue that the EITC is a much better way to help the poor. The other benefit of the minimum wage for politicians is that it makes low-skilled labor more expensive and boosts the demand for close substitutes, often union workers.
I find it strange that those who favor an increase in the minimum wage often are the same people who complain about outsourcing, or the moving of factories to low-wage countries or the greed of corporations such as Wal-Mart eager to squeeze every last penny out of their employees by paying only what the market will bear. Surely, such greedy and enterprising organizations will find a way to avoid the impact of the minimum wage by hiring fewer workers and finding other ways to reduce the cost of workers who are suddenly more expensive yet no more productive. I’m a big believer in the profit motive. I again commend to you this article at Coyote Blog that shows how a real business responds  to a sudden increase in the cost of labor.
Finally, let’s keep it civil here, folks. One of the things I like about this blog is the thoughtfulness of the comments on both sides of the aisle. Help us keep it that way by reducing ad hominem attacks on your opponent’s motives and IQ.