Spare us your histrionics. Forcing businesses to pay employees a wage determined by politics will either 1) be irrelevant because the the minimum wage is set below labor market rates or 2) cost jobs and, if the minimum wage is set very high, cause businesses to close.
Nope. There are two reasonable measures of value for a worker. One is the replacement value, which is the labor market rate. Another is the value to the employer, which is going to be greater than the labor market rate (otherwise, why hire?). Like any free market, the labor market sets prices based on individual negotiations, which means that if the employers have more negotiation leverage than the employees, they're going to drive the price of labor down, even if they're already making a nice profit.
A minimum wage changes the negotiating position of the employee, who can't agree to a wage lower than the minimum. If the employee simply isn't worth that much to the employer, that kills the negotiation. If the employee is still worth the higher minimum wage, then the employee settles on it.
Example: suppose I can hire somebody to do a moderately unskilled job that's worth $15/hour to me (or maybe $20/hour but $5/hour goes to miscellaneous expenses of having an employee). If I can hire somebody at $7/hour, I do. I get about $8/hour out of the arrangement, but if the employee asks for more I'll just hire another minimum-wage employee. Now, the minimum wage goes up to $10. It's still worth it to hire somebody at $10, so I do it. The difference is that I'm only getting $5/hour profit out of this.
The questions to ask here are how many minimum wage employees are only worth minimum wage to their employers, and the effect on the employers' finances. Minimum wage workers that aren't worth the new minimum lose their jobs, and businesses that can't function on the reduced profits go out of business. Obviously, if most minimum wage workers are being paid what they're worth, raising the minimum wage will have bad consequences. On the other hand, if most are significantly more valuable than that, they'll keep their jobs and the employers will be able to absorb increased wages. Since lower-paid people tend to spend more of what they earn than higher-paid people, raising the minimum wage can put more money in the hands of the lower-paid, and that can generate economic activity if the economy needs it.
So, the right minimum wage is significantly below what the average unskilled worker is worth to his or her employer.