harsh, thanks for your response, can you link me to the study? On the face of it, I think it is going with more assumptions than reality in those predictions and I can probably guess which assumptions they're making.
Productivity can/will increase with efficiency, especially in terms of non-human labour intensive tasks where things like computation may play a big role. If that doesn't translate into the work minimum wage employees do being more valued, then it simply shouldn't. The idea that you should only be paid what your labour is worth is straightforward I feel.
From the literature I've read (and this is not exclusively free market stuff) there seems to be far more to go towards minimum wage being harmful and only recent studies like Card-Krueger being held as some sort of opposition to what has been believed well established ideas on minimum wage. That Card-Krueger study was debated by Neumark-Wascher who showed that in actual fact, in their study, the minimum wage increases in New Jersey created ~4% decrease in employment. I'm wary of any amalgamation of the topic - especially when the methodologies can be abuse to suit a political stance - but if you have the study I'll give it a read when I have time.
Again, I restate: the demand curve is downward sloping, we know that if the prices are higher because the production costs rise (in this case it would be minimum wage) then less is sold because less people will be able to enjoy it. I'd contend that if raising the minimum wage has had little negative or no effect at all, then it could very well be showing that it has been kept artificially low (that is, in such an economy, even those low wage earners are valued higher by the market)* which would be another argument to abolish the minimum wage altogether. Or, that companies are becoming more efficient despite the restraints and being able cope with higher costs and while they have been able to eat the increases, they could very well be providing a good or service at a lower cost in which all people could enjoy and hence help the economy with the extra that they save. There are probably many, many more reasons as well where other factors are helping to lessen the effect of this negative law, but it does not mean it is not in itself a negative law nor does it argue for its adoption.
So before we throw out what is basically a universally held tenet (actually, it's termed "law of demand") amongst economists of all stripes, we'll need far more conclusive proof towards these effects to conclude that the minimum wage law is not negative in this respect. And I don't think that's possible.
*I guess this would be more a short term phenomena
EDIT: Actually found the main article I remember seeing a while ago, it's now hosted on webarchive: 50 years study on the minimum wage
http://web.archive.org/web/20110629183749/http://www.house.gov/jec/cost-gov/regs/minimum/50years.htm