The economic recession isn’t due to a lack of money in the market, but because the poor have no money. Essentially, the money isn’t circulating; it’s all been stuck in the banking system, turning into deposits and low-risk assets. No matter how much money the rich have, their consumption is still limited.
On the other hand, the poor want to spend but have no money, which gradually leads to excess production capacity in the market. This causes companies to start competing in a race to the bottom, driving profits to dangerously low levels, which sets off a vicious cycle. As company profits decrease, they scale back and lay off employees, making the poor even poorer, and savings become too risky to touch.
This is a quite silly way to look at the economy. Poor people by definition have no money, but there can be any single or combination of reasons that someone is in that position - they may be in a minimum wage job, live in a high cost of living area, have a big family to support, are only able to get less than full time hours, are deep in debt and potentially don't know how to use their income wisely. Some "poor" people could be given a million dollars and you return a year later to find them back down to zero, just giving them money is not a solution unless you teach them about proper finances and they are able to exercise reasonable self control. The poorest are generally not the ones propping up the economy at any time anyway, it's the middle and richest people that spend much more.