Economic theory suggest that when you increase the price of something (wages) the quantity demanded (workers) decreases, hence unemployment increases and if the price (wages) decreases the quantity demanded (workers) increases, hence unemployment decreases.
It might be a "stretch" but I think Elasticity of Demand for Labor factors into the equation.
Graph #2 shows the imposition of a new $9.00 per hour minimum wage ABOVE the current wage. This would establish a new PRICE FLOOR. This is a 24% increase in the wage rate. The quantity demanded for labor DECREASED to 75 workers. This is a 25% decrease in Quantity Demand for Labor. Using our formula for Price Elasticity of Demand (%chg in Qd/%chg in P) this suggests the Demand for Labor in this market is slightly ELASTIC, just over 1. If we apply the Total Revenue Test (in this case Total Income), we find that as the wage increased the Total Revenue (Income) DECREASED to $675.00. This suggests the Elasticity of Demand is ELASTIC—as the price increases the Quantity Demanded decreases by a greater amount.
Assuming Demand for Labor is relatively INELASTIC, even for low skilled workers in the short run, by increasing the minimum wage will increase total income earned by these workers.
If total income increases these workers have more money to spend. An increase in income will tend to move them to buy more “normal” goods and fewer “inferior” goods. Normal goods tend to be higher value goods purchased as income increases. Spending more money will create an increase in demand for new “normal” goods and services. Hence, businesses will sell and produce more goods and services. They will likely need to hire additional workers (at the margins) to produce and sell those additional goods and services.
Elasticity of Demand for low-skilled minimum wage workers seems to me mirrors the condition of the economy. If the economy is doing well and unemployment is relatively low, then an increase in the minimum wage may actually be productive for the economy, as the demand for that labor will be relatively inelastic.
However, in an economic downturn it seems to me the demand for low-skilled labor becomes relatively elastic and an increase in the wage rate will have a higher negative impact on employment.
Bottom line for me: Gotta pay attention to Elasticities and less to politics when it comes to this issue.