What this ultimately does is cause more money to be printed and released into the world. If the economy goes from $20 billion to $50 billion with no productivity there is less value for a dollar amount. True economic growth occurs due to an increase in productivity, not just larger numbers of cheap, paper bills being passed around.
I'm right there with you until you get to this part. The federal government doesn't print money to offset minimum wage, they print it to pay for government debts. It costs the government nothing to order employers to raise their wages at gunpoint, and the money supply does not need to be expanded to do it. However, the expanding money supply does create inflation that helps combat the effects below that I'm about to go into and help nullify the minimum wage penalty. So what happens if the money supply is not expanded and minimum wage is raised? Where does the money come from?
Optimally the money comes from the workers themselves. They produce more by taking on increased responsibility to offset their increased wages. So, for example, if someone is making enough money for the company to be worth $8/hr now, and the minimum wage is raised to $10/hr, then again
optimally, that employee increases his productivity by 25% to earn his new pay. As a result, the economy grows, and the employee's raise is coming entirely from the employee's productivity. How do you raise your productivity 25%? The most straightforward way if you're working 40 hrs/week would be to work 50 hrs/week instead.
What is more likely, is that with the increased overhead companies will have to either
raise prices or
lay off workers.
Raising prices is not a problem if all of your competitors have their overhead increased as well. If the entire market for a certain product raises prices simultaneously, and especially if that market isn't easily gone without by consumers, then the pay raise comes from the customers - directly offsetting something else they would have purchased. If, for example, the price of groceries goes up, then people will cut back on luxuries, and you see a shift in the economy where people in luxury industries get laid off as grocery workers make more money. When this happens, the consumers' standard of living goes down (luxuries traded in for necessities), the luxury industry workers' standard of living goes down (job traded for no job), and the grocery workers standard of living stays the same (wages go up, cost of necessities goes up). So the minimum wage made everyone a little poorer and actually shrank the economy.
Laying off workers is a great option if your labor force is easy to
outsource. If you can make all of your products in india or china and ship them over here for less than people cost here, you'll do that. As the cost of local labor rises (because the government raised it), outsourcing becomes more and more economical. People wonder why US industries outsource... well... minimum wage, social security, healthcare, these all make outsourcing very appealing. Outsourcing is the option of choice for most industries when faced with rising minimum wage.
In total, inflation actually helps offset minimum wage. 100 years from now when $10 doesn't buy a loaf of bread, a minimum wage of $10 would affect almost no one. But to make sure that it continued to have a negative effect on the economy, it would have been raised 20 times over that 100 years and be at $100/hr.