It sounds odd at first, but a minimum wage cut could actually help the US economy. Most get visions of falling incomes putting people into the streets because they will not be able to make their rent payments. This could occur if the wage cut was at the unsystematic level of risk (affecting only one party), but if wages fall on a systemic level (the entire country at the same time) it has the effect of strengthening the dollar and making the cost of goods and services cheaper for everyone.
What would be wrong if minimum wage fell by 5% and as a result everything got 5% cheaper to match? Even if prices only fell 4%, a tremendous amount of efficiency would be reflected in the currency markets nearly immediately.
California recently passed a budget which is cutting the pay of state workers by 5%. Additionally, there is talk that the Governor and legislature may have the same pay cut.
Greece recently enacted a 20% cut to the minimum wage which resulted in rioting. The cut goes so far that even pension benefits were cut 20%. Early on these measures are painful to a country, but the result is a country which does not have the ability to buy foreign goods unless they get dramatically cheaper. At some point foreign countries can no longer cut the price of exports and industry will begin to develop in Greece. Additionally, the Greek trade deficit will revert back towards a surplus.
Additionally, a lower minimum wage would encourage international firms to relocate to the country (whether it be the U.S. or Greece) if these firms can be rest assured that labor costs will be low.
Greece is worse off than the United States, but because of a rather similar debt to GDP ratio, it is very possible that the United States will have to follow suit with whatever Greece does, but to a lesser extent.
In conclusion, a minimum wage reduction in the United States would likely improve the economy by strengthening the dollar, destroying inflation, and improving the number of jobs available in the country. Few to no negative consequences exist other than short term, mild pain.
The U.S. Dollar index can be viewed in numerous ways, but one popular fund to gain or reduce exposure to the dollar is (UUP). Those who believe the U.S. will get tough and begin cutting pay might want to buy the dollar. Those who think that politicians will buckle under pressure may want to short the dollar.