Alright, I'll bite.
First I read Hayek:
[There is no reason] reason why the state should not assist the individuals in providing for those common hazards of life against which, because of their uncertainty, few individuals can make adequate provision. Where, as in the case of sickness and accident, neither the desire to avoid such calamities nor the efforts to overcome their consequences are as a rule weakened by the provision of assistance, where, in short, we deal with genuinely insurable risks, the case for the state helping to organise a comprehensive system of social insurance is very strong. There are many points of detail where those wishing to preserve the competitive system and those wishing to supersede it by something different will disagree on the details of such schemes; and it is possible under the name of social insurance to introduce measures which tend to make competition more or less ineffective. But there is no incompatibility in principle between the state providing greater security in this way and the preservation of individual freedom.
Then I read Rawls:
[T]he original position of equality corresponds to the state of nature in the traditional theory of the social contract... It is understood as a purely hypothetical situation characterized so as to lead to a certain conception of justice. Among the essential features of this situation is that no one knows his place in society, his class position or social status, nor does any one know his fortune in the distribution of natural assets and abilities, his intelligence, strength, and the like. I shall even assume that the parties do not know their concepts of the good or their special psychological propensities. The principles of justice are chosen behind a veil of ignorance... Since all are similarly situated and no one is able to design principles to favor his particular condition, the principles of justice are the result of a fair agreement or bargain...
Justice... begins... with one of the most general of all choices which persons might make together, namely with the choice of the first principles of a conception of justice which is to regulate all subsequent criticism and reform of institutions. Then, having chosen a conception of justice, we can suppose that they are to choose a constitution and a legislature to enact laws, and so on, all in accordance with the principles of justice initially agreed to... [A] society satisfying [these] principles... comes as close as a society can to being a voluntary scheme, for it meets the principles which free and equal persons would assent to under circumstances that are fair. In this sense its members are autonomous and the obligations they recognize are self-imposed...
[O]ne main task clearly is to determine which principles of justice would be chosen in the original position... I shall maintain... that the persons in the initial situation would choose two rather different principles: the first requires equality in the assignment of basic rights and duties, while the second holds that social and economic inequalities... are just only if they result in compensating benefits for everyone, and in particular for the least advantaged members of society. These principles rule out justifying institutions on the grounds that the hardships of some are offset by a greater good in the aggregate. It may be expedient but it is not just that some should have less in order that others may prosper. But there is no injustice in the greater benefits earned by a few provided that the situation of persons not so fortunate is thereby improved. The intuitive idea is that since everyone's well-being depends upon a scheme of cooperation without which no one could have a satisfactory life, the division of advantages should be such as to draw forth the willing cooperation of everyone taking part in it, including those less well situated... Once we decide to look for a conception of justice that nullifies the accidents of natural endowment and the contingencies of social circumstance as counters in quest for political and economic advantage, we are led to these principles.
In short, Hayek tells me that the state has a valid function to fulfill in providing insurance 'when few individuals can make adequate provision' and that this purpose is not incompatible with individual freedom. Rawls makes a very strong case that behind the veil of ignorance, moral and rational men would freely agree to basic principles of justice and equality because doing so is in their own interest. I think Rawls is right on that count. Because of the clear inability of any individuals to make any provisions for some sort of Rawlsian insurance, I'm going to channel my inner Hayek and suggest that perhaps the state should fulfill that function.