The "economics 101" ideas applied to price floors (which ie what a minimum wage is) predicts lower volume (fewer jobs/hours). It doesn't predict how much, so it still might be worth having a minimum depending on the demand curve (which is never really known). OTOH, even the biggest proponents of minimum wage would admit that at some level minimum wage makes things worse. Most would agree that a $1,000 minimum wage would cause unemployment. Still, there's no real way of determining the "correct" amount, and even proponents seldom come up with a figure.

Anyway, being the dismal science economists just don't have any good way of settling this. This isn't the first study on the topic. If you look at it from a meta-research perspective, it looks like a null result with findings on both sides.