Money doesn't just come out of thin air. Since increasing the wages for employment will come out of the pockets of the businesses, one of two things will happen to offset those costs.
1) The cost of goods and services will increase to offset the new (in some cases, close to double) wages for the same employee doing the same work. That means that the money people are making in the middle class, is actually worth less. So their wages go up. They drive the market for pretty much everything that's purchased in the US, so now they pay more for the same product, which means the people making that $15/hour are now also paying more for the same things they were before and they STILL can't afford the things they want or need.
2) The businesses will strive to be a "low price leader", so they'll retain their current prices on products. But they're not going to sacrifice revenue for being a good Samaritan. So lets say they have ten employees making $10/hour. setting aside all other overhead and assumed costs (i.e. healthcare, paid sick leave accruals etc) 10 employees making $10/hour means $100/hour total. Now all of a sudden that $10/hour is increased to $15/hour. The total cost per hour is now $150. But to keep the prices low, they have to get that cost back down to as close to $100/hour as they can. How? Require less people to do more work. Lets cut that back to 7 positions instead of ten. It's now down to $105/hour, and 7 out of 10 people are making livable wages. But what about the other three?
The point is, businesses are out to make money, and when you force them to increase their overhead costs per employee, they're going to figure out some way to offset those costs. Usually at the expense of the employee. So does it really help those living in poverty when in this example, you increase the wages of 7 people but put the other 3 out of work completely?