because of the minimum wage requrement and businesses' resultant reluctance or inability to afford them, the demand by the employers (not decreased worker demand) goes down, with the result that fewer workers are employed.

If this is the case, how do you account for the ubiquity of such businesses in every town and every city in the US? Service businesses (the ones that are more likely to pay minimum wage) can't exist without workers. Seems like if the minimum wage laws were resulting in fewer low paying jobs in the US, we would be seeing a decline in these kinds of businesses rather than the veritable explosion of such businesses that we see now in the US. The service sector is the fastest growing sector in the US job market.