More challenges and questions for minimum wage proponents

From Mark Perry of "Carpe Diem."

"At Cafe Hayek, Don Boudreaux recently posed several challenges for supporters of the minimum wage, and I added one of my own here on CD. In a new Cafe Hayek post, Don poses another challenging question for minimum wage proponents, and that inspired me to pose some questions of my own for those who support the
minimum wage lawgovernment-mandated wage floor that guarantees reduced employment opportunities for America’s teenagers and low-skilled workers.

By supporting a 40% increase in the minimum wage to $10.10 per hour, you have expressed your faith and confidence that politicians like President Obama have the abilities and knowledge to determine that $10.10 per hour is the correct or optimal wage for low and unskilled workers.

If you agree with President Obama and other politicians that a federally mandated wage of $10.10 per hour will improve the conditions of unskilled workers and generate net benefits for unskilled workers and the US economy, doesn’t it logically follow that those same politicians should establish minimum (and maximum) wages for all occupations in the economy?  That is, if a federally mandated wage of $10.10 per hour makes unskilled workers better off and generates net benefits for the economy, wouldn’t federally mandated wages for other (and all) skill levels also make sense?

Alternatively, is there something special about the unskilled labor market, such that politicians can determine and establish an “optimal” wage by government fiat for those workers, but something different about other occupations and skill levels such that those same politicians setting the minimum wage are unable to determine and mandate wages in other industries?

To be logically consistent, wouldn’t you have to either: a) support government-mandated wages in general for hundreds and thousands of occupations throughout the economy, including the minimum wage for unskilled workers, or b) reject the notion completely that politicians can or should set wages and prices, including the minimum wage? It seems to me that to support federally-mandated minimum wages but not support other wage and price control seems to be a logically inconsistent and indefensible position.
So my main question for minimum wage supporters is this: How can it be logically consistent for you to support politically-determined minimum wages for unskilled workers but not support politically-determined wages for all workers in all industries?"