Brad Delong thinks so.  Referencing a Bloomberg column from John Berry, DeLong let's us in on a presumed secret:

The word from inside the Federal Reserve is that Alan Greenspan is *not* optimistic about the dollar and *not* unconcerned about the U.S. budget deficit: that he was trying to express concern without triggering a dollar sell-off: that his words have been misinterpreted by markets as being more optimistic than they were intended to be.

OK, let's go to the tape.  The minutes of the December Federal Open Market Committee meeting include this information.

A number of participants voiced concerns about domestic and global financial imbalances. On the domestic front, such concerns focused on the magnitude of current and projected fiscal deficits, which seemed likely to keep national saving low. Views about the prospects for fiscal restraint in the years ahead were mixed; some participants believed that the odds of significant deficit reduction over the next few years were remote while others were more optimistic. Regarding global imbalances and the current account deficit in the United States, a number of participants expressed doubts that such imbalances would be reduced in the near-term. Better global balance would require not only greater national saving in the United States but also a notable strengthening in domestic demand among major trading partners. Such a strengthening seemed unlikely in the near term given the recent softening in the economies of several important industrial countries.

In the February 4 London speech that Berry references, Mr. Greenspan said the following.

... numerous issues that have arisen with respect to the adjustment of the U.S. current account remain unresolved. One is the effect of Asian official purchases of dollars in support of their currencies. Such intervention may be supporting the dollar and U.S. Treasury bond prices somewhat, but the effect is difficult to pin down. Another issue is the influence of still-growing globalization, arguably one of the key factors that has facilitated the financing of the U.S. current account deficit. There is little evidence that the growth of globalization has yet slowed.

The dramatic advances over the past decade in virtually all measures of globalization have resulted in an international economic environment with little relevant historical precedent. I have argued elsewhere that the U.S. current account deficit cannot widen forever but that, fortunately, the increased flexibility of the American economy will likely facilitate any adjustment without significant consequences to aggregate economic activity. That argument will be tested, I suspect, by possibly new twists and turns that will emerge in a seemingly ever-more complex international economic and financial structure.

So, the FOMC voices some concern in the official record of its meeting, followed by numerous speeches by Fed officials reiterating the point (as noted here, here, here, and here), followed by a Greenspan speech where he explicitly states that we are in uncharted territory with lots of uncertainty, while expressing the belief that the adjustments everyone agrees must come will occur in an orderly fashion.

And the issue is exactly -- what?  Is there any indication at all in any of this that the Federal Reserve is "unconcerned" about the either fiscal or external imbalances?  Is the assertion that internal forecasts or policy discussions within the Fed entertain anything other than exactly what Mr. Greenspan says?

One thing I've learned in my time at the Fed is to distrust any statement that begins with "word from inside the Federal Reserve."  God knows why financial markets react the way they do minute-to-minute, or day-to-day, or even week-to-week.  I have as little insight into that as I do into why it is considered a scoop if opinions that are completely transparent are repeated in hushed tones.