The D.C. city council is doing this, not the federal government:
The district's city council has passed a bill, awaiting signature of Mayor Vincent Gray, specifically targeted to block the company. It raises the district's minimum wage to $12.50 per hour only for stores with more than $1 billion in sales and store size of more the 75,000 square feet.
Yes I am aware of that which is why I put this in my post
First I will question where does a city government get the authority to set wages for private entities. .
The question of where does the federal government get the authority to set wages was an aside to the larger issue of the federal minimum wage. Which is I imagine where the city gets the stupid idea.