Regardless of one's position on the minimum wage, there should NOT be a Federal minimum wage. This should be left to the individual states and territories. A minimum wage that might be just fine in San Francisco, is a stupid idea in...oh...Samoa, for example. Each state has different circumstances and imposing the same wage on all is biased against the poorer states.
You win the prize for being true to the Constitution.
Nowhere does it say,"...and there shall be a department of
labour...department of Housing..." etc etc.
The USA is a democracy/mobocracy. The Constitution,
is dead.