I'm not going to do your research for you <G>, and I'm not sure I believe a minimum wage is "worthless."
It's a really long topic for discussion. But the basic overview (AIUI) runs along these lines:
A worker's own self-interest keeps the boss from royally fucking him. If he isn't satisfied with how much he's getting paid, he's free to get another job. If no one else is willing to work at that rate, then the boss has to make a better offer.
The idea behind strikes and unions is very closely tied into this. If you have useless dangerous jobs that you could train a chimp to do, and feel like it would be worth $1 an hour to have a human do it instead, that worker really does not have any bargaining power. If all your valuable skilled workers go on strike to get him some safety equipment, it's a lot more likely to happen.
With no minimum wage, if you have three cushy jobs that are worth $3 an hour to your business, you could hire some unskilled teenagers to do them at that rate. They get cushy jobs and start gaining experience in the work force (which is a really important thing to keep in mind). With minimum wage, you have to hire one person to do all 3 jobs, which makes them a lot less cushy and destroys two jobs.
That "gaining experience in the work force" is a really important factor to consider. In a lot of ways, we're still in the middle of the worst economic disaster since the Depression. We have a lot of kids in their mid-20s who are living at home and have never had a job. The entry-level ones they should have worked in high school are filled with people in their mid-30s or 40s who are desperately trying to support families. This kind of long-term unemployment is disastrous for many aspects of their lives. If they could get some job, any job, for $2 an hour...I suspect most would turn their nose up at the chance. But I'm sure some would jump at it.
In my mind, that's kind of where the argument loses at least a little steam. With no minimum wage, the bosses could fire the middle-age people and easily replace them with eager younglings for, say, 1/3 the price. But, if they're willing to do the work for less, shouldn't that option be available to them? I mean, this seems like basic "supply/demand" and "right to make your own decisions about how you spend your time" to me.
In a lot of ways, that ties in with the idea that illegals "steal" American jobs because they work for so little, undercutting minimum wage. There may be some truth to this. I don't really know what (if anything) it says about the minimum wage discussion. OTOH, I've worked for a few people who strongly preferred hiring illegals. Not because they're cheaper (we got paid the same) but because they work so much harder.
Personally, I think minimum wage is, at best, a band-aid on a much bigger problem. We get focused on questions like it and ignore the more fundamental questions. (Whatever they may be).
I know this isn't the answer you're looking for. But hopefully it's a little more useful than Arlet's.