Cite, please.
Often analytical (rather than emotional) minimum wage proponents admit a small decrease in total employment but think the benefits to those who make the cutoff helps offset that. That might even be true in a growing economy with generally low unemployment and short unemployment terms. In one with ~20% youth unemployment, and workers discouraged by multi-year stints of unemployment, any job – even a low-paying job – is better than prolonged idleness. Employers are understandably loathe to take a chance on those who have gone years without a reliable work history, or never started a work history at all.
When he wasn't quite as partisan, even Krugman could make an eloquent case that bad jobs at low wages were better than no jobs at all at wishful-thinking wages. See for example:
In Praise of Cheap Labor: Bad jobs at bad wages are better than no jobs at all
http://www.slate.com/articles/business/the_dismal_science/19...
Even today, while Krugman is against any sort of lowering-nominal-wages or lowering-minimum-wages for macroeconomic adjustment, he'd like to achieve the same thing through massive fiscal and monetary stimulus, essentially lowering wages through inflation.
In the funhouse mirror world of politics, the 1-2 punch of higher minimum wages but also inflation is a perennial winning strategy. Give people a superficially popular, though actually harmful, boost in minimum wages: an easy focal point on which to campaign. But prevent its full damage with harder-to-assess, noticeable-only-after-the-election inflation. Or at least keep the celebrated raises below other growth/income indicators, so that it's mostly a symbolic measure. (Any raise large enough to make a 'big difference' for minimum-wage earners would also make a 'big difference' in boosting unemployment.) Via the only-slightly-harmful symbolism, everyone (who is a politician) wins!
Pretty much right now minimum wage workers usually do service jobs (fast food, waiting, etc), household chores (cleaning, landscaping), farming, or no-skill manufacturing.
No-skill manufacturing is largely dead in this country. Changing the minimum wage won't change the fact that you still have to follow environmental and safety regulation. That is expensive in its own right. You also can pay $3/hour in a different country and get good people. You can pay $10-15/hour and get great people. If you pay $3/hour in the US, you are going to get the people who can't even get a minimum wage job. I doubt a lot of companies want to hire those people for any price.
For service jobs, you usually have a fairly fixed number of people. If McDonalds has 3 registers, they already have 3 cashiers at lunchtime. Lowering minimum wage just hurts all those people because the pay will be less. It won't create many more jobs.
Farming could see a big increase in people, or at least a big increase in paying people on the books. A lot of migrant farmers are paid off the books below minimum wage as is.
So where is this giant pent up demand for hiring $3/hour workers? All I see is a marginal increase in jobs, and a massive decrease in wages for everyone else near the bottom.
There are some people who can only be hired with a wage below the minimum:- high school dropouts, immigrants, physically disabled, blind, mentally ill, elderly, long term unemployed. By setting up a minimum wage too high you are ensuring all these people will not get jobs even if they want or need one. To the employers eyes: if you had to pay $7/hr anyway to hire someone, you might as well hire someone who is physically strong, understands english and has graduated high school.
The minimum wage makes people on the lowest tier unemployable. Arguably it does raise wages for workers on the people near the bottom but not quite there. As you can see there is certainly a trade-off to be made.
All you are saying here is that the min wage is harmless because it's set below market rates. I.e., it's like setting a $0.25/gallon price floor for petrol, or passing any sort of "keep doing what you are already doing" law.
But if that is the case, then why would wages decrease if we eliminated the min wage?
As for the pent-up demand for $3/hour workers, you can see it every time a company outsources or offshores. My company (located in India) wouldn't exist if we had to pay $7.25/hour, for example. (Of course, market rates for the people we need would probably be higher than $7.25 in the US, so the min wage is a moot point - lowering it would not affect our costs or our hypothetical US employee's wages.)