If you have ever taken an Econ 101 class at University, you were probably taught that minimum wage laws have the undesirable effect of increasing unemployment. The logic is straightforward, if you increase the price of anything the demand for it goes down. Your wage is just the price of labor and if the government sets it artificially high employers will find ways to hire fewer workers.
But remember something else your economics professor probably told you once, but then ignored for the rest of the semester. The magic workings of the market hold only under certain unrealistic assumptions, such as perfect competition.
In fact, our economy is highly monopolized and the buyers of labor power, i.e. employers, have greater bargaining power than workers. This means that, in the US, in most cases, wages are held artificially low.