There's no "free lunch" or something for nothing like the President believes.
Indeed, the Federal government has no business setting wages in the first place!
From American Enterprise Institute,
More than 500 economists, including three Nobel laureates (Vernon Smith, Eugene Fama and Ed Prescott) have signed this letter arguing that artificially raising the minimum wage to $10.10 per hour through a government mandate would have adverse effects on the employment opportunities for unskilled and low-skilled workers. The tragedy of this well-intentioned, but misguided legislation is that it would harm and disadvantage the very workers it is intended to help.Why? Well, if you increase the cost of something like Labor, the demand for Labor goes down. It's illustrated by a simple diagram from Economics 101 shown below from Mark Perry at AEI. The horizontal axis is the quantity of low skilled labor and the vertical axis is the unit price of labor. The graph shows equilibrium between supply and demand at the current minimum wage of $7.25 per hour.
If the price for lower skilled workers goes up (with no corresponding increase in skills or productivity), the demand for workers goes down as the supply goes up. The new equilibrium is at the labor quantity E1, down from E0. The quantity of jobs declines. Even common sense would tell you as much.
With an artificial increase in the lowest wage, it will be harder for marginal workers like inner city kids, who are trying to get their first job, to find one. For many high school dropouts in certain areas, the current $7.25 per hour rate is already too high. Like I said, the government needs to get out of the wage setting business.