For all that I think there are huge weaknesses in Rawls' theory. Essentially, his method is based upon taking two methodological assumptions and stretching them far beyond breaking point. His theory also doesn't answer the question of how we should help the poor and doesn't answer Nietzsche's great challenge to any theory of justice.
Assumption 1: Determinism
Just as science has roled back the number of everyday phenomena that religion is called upon to explain it has also rolled back the domain of free-will. If people make their choices because of their upbriningings, genes, vitamin deficiencies or brain chemistry what right do we have to punish them for their bad luck? Murderers tend to have similar differences in their brain chemistry. Why would we punish them for having a malfunctioning brain?
The problem is that there are huge gaps in our understanding of how the mind, and the physical world, works. Much that appears to be causing certain behaviours could actually be a response to it, or correlated with it but not a cause. There is plenty of room for free will yet. Once free will comes back into the picture Rawls' thought starts to seriously weaken. If someone chooses a less moral path they can deserve less favourable treatment.
Of course, that isn't true of many of the poor. Many of them did have an awful start and little chance to prove their quality. However, allowing some roll for free will both implies a more nuanced and discriminating policy than blanket redistribution and makes the proper question for any policy aimed at helping the worst off "how can we give people the chance to show their moral quality?"
Assumption 2: Risk aversion
People will usually, ceteris paribus, prefer to take less risk. I can believe that if, in an original position, they were offered a choice where most would be poor but a few would escape to relative riches they'd choose to make the poor better off at the rich's expense. However, your actual chances in society today aren't like that. Most people will be middle class and, while hardly raking it in, basically pretty alright. There is a core of 1/6 to 1/4 of the population who are in a pretty wretched state. There is then a small but significant portion of the population who do very well for themselves.
If faced by that choice I'm not convinced that most people would really want to pay that much to insure themselves against the possibility of poverty. They'd want to ensure that they are kept alive and in reasonable comfort against the elements but wouldn't want to hurt their fortunes if they drew the most likely result (somewhere in the broad swathe of the middle class). I'm not quite sure why I think this but it seems intuitively sensible to me and, here's the real beef, I know just as much about how people would feel in the hypothetical world of the original position as John Rawls or anyone else does.
How should you help
While I disagree with Rawls that doesn't mean that I don't see helping the poor as a broadly good thing. However, that doesn't necessarily imply a case for redistribution. The Citizens Basic Income can't do a lot of redistribution without becoming cripplingly expensive. It is more plausible as a safety net. Other forms of redistribution can hurt people's incentives to leave the unpleasant situation that is welfare dependency. In that way it can make them worse off.
Chris Dillow argues that the difficulty of using improved educational standards to create opportunity for unfortunate children shows that we should give up on educational opportunity. I'd argue that even if this is true (and I think that reform can make a significant difference) it doesn't imply that we should discard attempts to give people an opportunity to better themselves. Instead, it implies that other measures besides improving the education system have to be tried as a part of any coherent attempt to give people real opportunity. That's where the work of thinkers like Theodore Dalrymple and labrador conservatism comes in.
Art is cruelty. The quest for excellence and beauty for its own sake and in an attempt to understand the nature of humanity and the good life is expensive and impossible to justify under the Rawlsian system of justice. A Rawlsian may justify high culture on the grounds that it does some nebulous good for the economy or on some other spurious rationale but they are not being true to their principles. While a liberal Rawlsian might tolerate art they cannot really value it without admitting the bankruptcy of Rawls' ideology.
Nietzsche saw that art meant cruelty but chose art nonetheless. Any culture that is to be truly worthwhile has to make this choice, at least occassionally. Otherwise it denies what is best and most praiseworthy in humanity.
"Without art we would be nothing but foreground and live entirely in the spell of that perspective which makes what is closest at hand and most vulgar appear as if it were vast, and reality itself."