At least some of the budget would come from realizing reductions in bureaucratic overhead from eliminating the welfare apparatus and costs associated with crime (which poverty is the biggest predictor of).
We also always seem to have enough money to bomb the ever living shit out of brown people in all the far flung regions of the universe, so I don't understand why cost should ever be an issue.
I don't think need is either an important issue. The problem with your last sentence is that it "no right to income" implies "no right to feed one's self", i.e. "no right to live." Do people deserve to starve to death just because they are lazy?