The empirical evidence provides little support for claims that minimum wages boost economic growth or alleviate poverty during downturns.
Source: Why the Minimum Wage Can’t Solve the Poverty Problem - Foundation for Economic Education
Despite the fact that when adjusted for inflation minimum wage is well below it's maximum in the late 1960s, there is less poverty now than there was then. The problem is that while a higher minimum wage may help a relative few in the short run, it hurts many others by increasing unemployment and reducing the opportunity for those who make lower wages to progress to higher earning positions. It can also lead to higher prices thereby further harming those at lower wage levels. Those promoting an arbitrary high minimum wage fail to take into account all but the most immediate economic effects.