When minimum wage rates are set above what the market rates would ordinarily pay, costs per worker are held artificially high. This keeps businesses from hiring workers they otherwise would, thus reducing hiring and keeping unemployment levels at artificially high levels.
When costs are artificially higher than they otherwise would be, certain profitable projects are no longer profitable, and otherwise fruitful investments are not made as a result. The economy as a whole thus grows at a slower rate than it otherwise would.
While the benefits of removing minimum wage are felt by most of society, those who currently receive minimum wage would feel pain in an immediate removal of the minimum wage. A gradual announced phase-out of the minimum wage is the best method of reducing the impact on these workers. This would allow current workers to plan ahead and would encourage them to increase their productive value through education, while at the same time allowing businesses and the unemployed to benefit from new hires at a market rate.
If this move is deemed too politically unpopular, stimulus funds could be diverted from TARP in order to fund the difference between new worker wages and the current minimum wage. Of course, this method is much more susceptible to fraud, but it could be the only politically plausible method. Furthermore, methods could be put in place to minimize the scams (e.g. only a portion of the shortfall between the current wage and the minimum wage could be subsidized, and it could only apply to newly created positions).
For businesses to grow, profit opportunities must exist. An easy way to increase profit opportunities (and thereby ease the pain of this recession) is to remove the effect that minimum wage has on businesses: artificially higher costs that discourage investment. If the government has the political will to continue to stimulate the economy, TARP funds could be used to subsidize those who would be negatively affected.