The dollar remains strong in the face of our economic woes in large part because our currency is viewed as a safe-haven in times of global financial crisis (such as now). The irony of this is that when you combine worldwide demand for dollar growth, and the worldwide tendency to hoard currency / save and not spend (on US goods or assets), what you get is the increased likelihood that the appreciated dollar will make our recession longer and harder than it might otherwise need be. Particularly if the recession improves faster abroad than in the US (which may be likely since the US was the major source of the downturn and the many other countries are only being affected indirectly)we may see some of our trading partners start turning, at least during some transitional timeframe, to countries with less expensive currency: only furthering our export issues.
Over time one would think the financial cloud would clear, spending would resume and dollars would be used for their purpose, but this won't happen over night. There will be a transition with x number of economically-improving countries that will shift from buying from the US to buying from cheaper-currency countries, and y number of less-improving countries that will continue to hoard dollar currency for a time.
Treasury Sec. Geithner believes in a strong dollar as a signal of confidence in the US market, but it seems that this is causally backwards. The strong dollar isn't signaling confidence, it's the already existent confidence in the dollar relative to other currencies that is causing the strong dollar. The sustained strength of the dollar will have little to no impact on US market confidence, particularly if the rest of the US data continues to plummet.