Increasing the minimum wage wouldn't help the poor because there will be a ripple effect that results in the increase of prices and future unemployment. In order to actually help the poor, new money would have to given to the poor with no strings attached. Just as the Cantillion effects gives the government and the elite new money with no strings attached, the same can be done for the middle class as well as the poor.
But the government wouldn't do that because of greed. Money is just a mechanism for the government to seize real assets from the people.
Awesome comment @snoreball