I agree with most of what you say. I don't want the minimum wage raised and yes unemployment is about perfect* right now.
But if you are going to discuss economics in the cause-effect way that you are, do you have a source that shows how strongly the correlation is between the unemployment rate and minimum wage? I'd suspect that the correlation isn't actually as large as you may believe. I'd also suspect that what does correlate much higher is employment levels and inflation. So people may still be able to get jobs if the minimum wage raises, but the increase in wages inflates the money where the increase in minimum wage isn't an increase at all.
*Most economists in the US point to 4.7% as an optimal value for unemployment. This is refered to as the "natural rate of unemployment" where people are naturally in between jobs as jobs are created and destroyed continuously in a healthy economy. Any rate below 4.7% and economists start worrying about inflation... so unemployment that is too low is usually a concern for economists.
Edit: I realized I was a little off-base there.
Yes, raising the minimum wage causes rising unemployment, even though the correlation won't be that strong. Raising the minimum wage hurts those willing to work at the minimum wage (less jobs available), the majority of people won't be directly affected. But where they will be affected is the price of goods. Small price increases at Wal-Mart and fast food chains will lead to price increases in general, hence inflation.
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