There's reasonable concern by people — e.g. Warren Buffett — that low domestic savings rates for long periods of time will ultimately prove unsustainable, and will be corrected by a real depreciation in the dollar. This analysis takes place over a period of time for which money is typically supposed to be neutral; would a highly interconnected region of the United States experiencing a sustained (but unsustainable) low savings rate be expected ultimately to see local prices rise (and wages fall) relative to prices (and wages) nationally? I guess it seems reasonable. I might want to think about more details of the likely nature of such an imbalance.
If Arizona and Florida are, for some reason, less relatively conducive to productive work than to retirement than the rest of the country, you could see a sustainable low savings rate as current wealth flows to those states indefinitely. I suppose prices might end up higher there because of that, but if real wages rose to the same levels as the rest of the country, the comparative advantage in retirement would presumably wane.
The question of "sustainability" is likely more one of the stock of wealth accumulated than of purchase-related flows; in the case I just gave, the sun states are never in debt to the rest of the country. "Wealth", though, is hard to measure; net wealth is a concept related to expected future creation of consumer goods, not past flows (what you might call the "cost basis" of that wealth). In many contexts, especially on a large scale, one might expect one to proxy the other fairly well, but it is a macroeconomic fact that foreign investment from the United States tends to take the form of equity, while foreign investment from many other countries — certainly from Europe to the developing world, and from the rest of the world into the United States — more often takes the form of debt, such that observing changes in net flows of investment income makes the United States look like much less of a debtor nation than you would expect from looking at past trade deficits. (I.e. U.S. investors see a higher rate of return on their past investment than foreigners do.) Little in economics is very backward-looking; the past is relevant insofar as it informs the future. These forward-looking indicators should be more meaningful.
This still doesn't answer my title question, though; what is the impact on me of my neighbors' not saving enough money? I still need to think this one through.