Actual measured results from minimum wage increases are not that simple. Most recent studies have shown no or minimal increase in unemployment with minimum wage increases, because low-wage jobs are inelastic (garbage will get emptied, toilets scrubbed whether or not the minimum wage increases). Of course it depends on the amount of min wage increase.
One counter-intuitive effect of minimum wage increases is to increase overall economic activity by putting more money in the pockets of people who will certainly spend it ("priming the pump").
See
http://en.wikipedia.org/wiki/Minimum_wage for a nice non-simplistic overview.