The minimum wage debate is in relation to the hiring of illegals. As I previously stated, employers who hire illegals do not have to abide by the minimum wage law, or any other employee legalities for that matter. Therefore, since you're against the minimum wage, you should have no problem with employers who hire illegals in order to evade said law(s).
The illegal day workers that are hired throughout the country demand and get more than the minimum wage because of market forces.
The minimum wage is for touchy feely individuals who have no clue about free market capitalism.