I've been thinking a lot about basic income schemes lately, which do exactly that for everyone (not just the poor, though they'd benefit the most). You calculate how much it costs a person to pay their basic living expenses: food, a decent place to live, maybe a transit pass. Then you pay everyone in the population that amount of money each month, unconditionally (no means testing).
I once calculated that such a system, if applied in Canada, would require something like a 36% flat income tax if it were entirely funded that way, and it would have a break-even point at about $65k annual income (below that, you receive more than you put in). I expect the situation in the US to be similar.
Part of that cost could be offset by reducing or eliminating existing welfare and social security programs, including food stamps, employment insurance, and subsidized housing. It would also let you eliminate minimum wage, since you no longer have to be concerned about wages covering basic living expenses.
There are a lot of questions about how this would affect an economy. Would it cause massive inflation? Unemployment? Substance abuse? Or would it be the most effective social program ever? I have no idea. But I think it's worth a try. My hunch is that you will see all of those negative effects increase somewhat (inflation, unemployment, substance abuse) or in some people, but that the positive effects will greatly outweigh the negatives.
You needn't implement it all at once. You could apply it first to a random sample, say 1% of the population. Those people receive basic income and pay the tax required to fund it. They would also become ineligible for the social programs that would be removed if you rolled it out nationally (the details of that part may be tricky). Only roll it out to the whole population if the results are positive after a few years.