With the minimum wage in the air, I see the Econ 101 trolls are out in force. Look, unless you believe that the labor market is accurately characterized as perfectly competitive then not only is it the case that the minimum wage doesn't necessarily, reduce employment, it's actually quite possible that small increases in the minimum wage will increase it. To the extent that firms have market power, and there's plenty of reason do think they do, the impact of small minimum wage increases can potentially be either "paradoxically" to increase employment or to just basically be a wash. You can read Alan Manning's book if you're interested in more, or if I'm extra inspired later I'll given you the Econ101 version of monopsony (sadly, not always actually taught in Econ101) so that even smart Ph.D economists can understand.
The real point is that if the minimum wage has small or negligible employment effects, and there is both theoretical and empirical support for this idea, then it's a pretty effective and inexpensive poverty reduction program. Obviously if poverty reduction programs for poor people interest you less than, say, poverty reduction programs for oil executives then you don't much care about that.