Before suggesting some new examples of LLFMs, I'll say a word in defense of minarchism. It's obvious that while this administration touts small government, in the realm of doing it has actually created a fiscal mess of historic proportions — but their lack of competence (or what have you) is not in itself an argument against small government policy. I fear that the growing frustrations and ad-hominem obsessions of the Left are causing progressives to confuse ideas with people. Consequently, babies are in danger of being thrown out with bathwater. Now, I will not specifically defend "supply-side" economics. (It is potentially subjective whether you are on the right or left of the Laffer curve maximum, and correct supply-side policy only cuts taxes when you are on the right side of the maximum. Likewise, the results of such policies are difficult to prove since experimental controls are lacking. Perhaps tax receipts increase but would have actually increased more without the cuts. Perhaps any economic growth subsequent to implementation is a result of other liquidity factors such as interest rates.) Nonetheless, I don't think the basic insight of the Austrians is at all in question: that decision-making is better distributed to the many individuals who are affected by the decision(s), rather than entrusted to a distant, semi-interested authority possessing vastly less knowledge. The latter situation will inevitably result in more shortages and gluts, even if incentives are not a problem.
I am however a utilitarian first and a minarchist second. Economic efficiency is a mean to general happiness, not an end in and of itself. Now you can certainly compile a list of problems with strict Utilitarianism as we did in our undergrad philosophy classes, but I will just say that I am not an absolute Utilitarian, and I think that will suffice here. Critics of small government thinking must be careful not to mistake ideas for people and bad examples; proponents must take care to not mistake means for ends.
To me, the question posed by Katrina is not so much a general problem of big vs. small government, but more importantly, of effective government. To a large extent, the size question applies to the government's role with respect to many types of insurance, disaster relief being one of them. Which sorts of insurance should have compulsory payments and/or universal coverage, if any? How does insurance differ from infrastructure, like police, roads and courts? Those are clear, specific versions of the question.
In terms of risk-sharing, many of our practices will someday be looked back on as medieval medicine is now regarded. Advances in communication have made it possible to quickly share risk with low transaction costs in a many-to-many manner, but this is just being dimly realized, especially where politics are involved. In addition to more traditional forms of private and public insurance, I have here introduced the concepts of tax and subsidy insurance. People should be able to hedge against their taxes, and every piece of tax and subsidy legislation can be described in terms of its "implied tax effect" on every taxpayer. (This framing alone encourages fiscal responsibility.) With subsidies, legislation-linked futures markets would allow two types of hedging/insurance to occur: 1) the potential recipient could sell futures representing the probability of receiving the subsidy, and 2) every other taxpayer could buy the probability of passage, thus hedging against their implied tax loss if the subsidy is granted.
Furthermore, legislators should welcome these markets as they will help to dissolve political log-jams by allowing private entities to meet each other "half-way" through their hedging. "Pork" will be a lot less painful to cut from budgets — and there is plenty of pork still out there despite what some people say. Democrats should attack on this point and Republicans should co-opt them, retaining the better parts of their small government thinking. Legislation-linked futures markets would help to unwind all these questionable subsidies and put a dent in the spending side of the creeping fiscal crisis.