The current program is TANF, Temporary Assistance for Needy Families, which does not provide ample benefits to put people above the poverty line (i.e., for a single person= $11,000; for a familiy of 3= $38,000). The poverty line is calculated using a terrible equation, essentially, by mutiplying a minimal subsistence diet (something you would get sick on if you lived on it for 5 years) by 3. Data has found that you actually need to multiply this number by at least 5, and probably need to adjust for a more nutritional diet, that doesn't make you ill.
Also, poor people do pay taxes, at least 7% of their income goes to taxes. Everyone pays taxes.
Welfare is federal aid to those that qualify, but less than half the families who qualify are given aid, even though our poverty stricken populations are increasing.
Benefits include cash (average $350/month per family), food stamps, and Medicare/Medical. Even with ALL of these benefits, TANF does not help people out of poverty. While child poverty rates have risen (23% in America, 10% higher than 30 years ago), federal assistance has gone down (even though the benefits are MEAGER at best).
People who are below the poverty line are not riding free; they do not want to be there, and most people are on TANF for VERY short time periods. People end up there because of life events: divorce, job loss/unemployment, illness, etc.
The federal government gives more money to the rich than the poor ($7-13 billion/year); it would take 50 years to equal that money in welfare.