(Since my attempt to make a point in a somewhat offhand and popularizing way seems to have been at the expense of clear communication, let me have another try, this time in a duller and more academic mode.)
Rawls has an idea of a feasible utopia, a well-ordered society, taking the form of a property-owning democracy, in which distributive outcomes are programmed into the basic institutions via incentives attached to rules such that citizens, pursuing their own good within those rules, are led to bring about those outcomes. Importantly, those outcomes have the properties that they guarantee the worth of the basic liberties to citizens (material inequalities don’t undermine political equalities) and the difference principle is satisfied. This conception of what the just society would look like is important in responding to critics like Nozick, because, contra Nozick, the holdings that individuals have in the Rawlsian just society result from history: people are entitled to what they have because they have the rewards that have come from some action specified in advance by the rules (such as a net salary for doing a certain job or the winnings associated with a fair bet). However the system as a whole is designed such that the invisible hand brings about just (or at least tolerably just) outcomes. A Rawlsian feasible utopia therefore satisfies someone like Hayek’s understanding of the rule of law: the government isn’t constantly intervening, trying to realize some antecedently decided-upon distributive pattern; rather the preferred distributive pattern emerges automatically from the normal operation of the system. Of course, this isn’t exactly laissez-faire: since the government does have the job of constantly adjusting the rules (such as, but perhaps not even mainly, tax rates) because left to itself entirely the system would drift away from its distributive “target” and the political equality of citizens would be undermined.
My intent in the foregoing paragraph is purely expository: it aims to be an uncontroversial (though necessarily incomplete) account of what Rawls believes about the functioning of the basic institutions of a just society. There are a number of things one could say about Rawls’s view here. In particular, I think that it is wildly overoptimistic about our ability to design incentive schemes with more-or-less predictable outcomes. Duncan J. Watts, in his recent Everything is Obvious ,  is eloquent about the contrast between our confidence in our ability to design incentive schemes that will, say, raise the poor out of poverty, and our actual record when we’ve tried. To the extent to which our capacity to program such schemes is limited, I think that egalitarians will need to make more use than Rawls would have liked of ex post pattern-aiming administrative redistribution and that such ex post intervention will violate the norm of prospectivity that people like Hayek believe essential to the rule of law. If I’m right about that (and of course I might not be) then egalitarians face an uncomfortable choice between better conformity to their egalitarian goals and closer adherence to the norm of prospectivity. I favour more equality even at the expense of reduced certainty, others will disagree.
But there’s a further point, which we can call the problem of Rawlsian transition which, in my opinion, would exacerbate the tension, even in the event that we could solve the design problem for a feasible utopia. Rawlsians tend to see existing liberal democracies as legitimate but unjust. What I mean by this is that they think that those liberal democracies pass a threshold test of legitimacy such that claims and duties established under their basic institutions are valid. If I use the money I’ve earned through my work to buy a yacht, then I’m entitled to my yacht and it would be unjust for you to take it off me, even though the system under which I transacted falls a long way short of what justice requires. And just as it would be unjust for you to take my yacht, it would also be unjust of an incoming egalitarian liberal government to seize it, because I acted, in good faith, in conformity with the law, to get what I got. Now clearly, my holdings are not protected if they result from force or fraud on my part. But “force or fraud” here has a reasonably specific legal meaning. Tempting as it might be to claim that the 1 per cent (or the 1 per cent of the 1 per cent) acquired their holdings illegitimately, I take it that that’s false in the non-rhetorical sense: they enriched themselves according to the rules (notwithstanding that the rules were in part shaped by their lobbying). My worry now concerns the transition from the existing bad distribution to a Rawlsian feasible utopia: could it be achieved in an acceptable time (say a couple of decades at most) whilst relying exclusively (or with “notably rare exceptions”) on adjustments to the rules, incentives, etc that citizens face prospectively and the payoffs associated with them? Or would it be necessary (in violation of the norm of prospectivity) to take from some and give to others?
My worry about achieving the transition by redesigning the prospective rules has two components. First, a concern about whether, if everything went smoothly, such adjustments would shift the distribution of wealth and income sufficiently in a reasonably short time. And by “if everything went smoothly” I mean (a) we get the design component, that I expressed skepticism about above, right and (b) the 1 per cent only use their ingenuity and that of their lawyers and accountants to hold onto their wealth and eschew extra-legal action and political resistance. Second, a concern about political resistance by the 1 per cent: whether it would be possible to sustain such a transition over the time it would take, in the face of inevitable setbacks which the 1 per cent would exploit. The coming to power of an egalitarian liberal government, determined to effect radical changes in the basic institutions of society to the detriment of the 1 per cent would surely cause financial panic and economic dislocation. Such a government would then have to choose between abandoning its programme and carrying through quicker and more decisive measures to break the power of the 1 per cent, measures which would certainly violate the norm of prospectivity. 
My thoughts here include an assumption that some people will reject, so it is best to make it explicit. The assumption is that a Rawlsian just society would be very different from our existing liberal democracies in its pattern of wealth and income and indeed in other respects including the ownership and governance of firms. A species of “left” neoliberal, of which Matthew Yglesias can stand as a representative example, would surely disagree. Though they reject the existing wealth distribution as having become dysfunctionally extreme, they probably take the view that a “cleaned-up” version of the status quo, because of capitalism’s capacity for innovation and growth, would work to the greatest benefit of the least advantaged. To the extent that they are right and “feasible utopia” is closer at hand that I think it is, my concerns lose their force. Whether or not they are right about the facts, though, I take it they are wrong about Rawls, whose ideal of a property-owning democracy was more radical than mere welfare-state capitalism. 
fn1. On which, see (recommended!) Martin O’Neill and Thad Williamson eds, Property-Owning Democracy: Rawls and Beyond (Wiley-Blackwell, 2012)
fn2. The clearest Rawls text on this is probably, “The Basic Structure as Subject”. See also ch. 1 of Thomas Pogge, Realizing Rawls (Cornell, 1989).
fn3. Chapter 1 (in the Kindle edition, loc 361 et seq).
fn4. On these latter points see, for example, the reflections of Oskar Lange on the transition to socialism (a different transition, to be sure) in Lange & Taylor, On the Economic Theory of Socialism (McGraw-Hill, 1963) pp. 122-7.
fn5. Again, see O’Neill and Williamson.