Krugman today insists that we do, in fact, face a problem of inadequate demand. And he's right! But he glosses this as an "excess supply of savings even at a zero interest rate," which isn't right at all.
Let's be clear: There is not "an" interest rate, certainly not a zero one. There are various interest rates, and the ones that are relevant to saving and investment remain high. The BAA corporate bond rate (the red line in the figure below) is currently at 5.7 percent -- pretty much exactly where it was in the first half of 2005. And given that inflation is substantially lower than it was five years ago, that particular real interest rate is not only not zero, it's gone up.
The real question is, can reducing the federal funds rate reduce the economically important interest rates? Now, obviously the answer is No if the fed funds rate (the blue line in the graph) is as low as it can go; in this sense the ZLB is real. But the answer can also be No when the fed funds rate is well above zero, if there's no reliable link between the overnight Treasury rate and the rates businesses borrow at; and that seems to have been the case since sometime in the '90s. As the figure shows, the Fed's recent rate reductions didn't reduce bond rates at all, even before the Fed Funds rate hit zero; and all the hikes earlier in the decade didn't raise bond rates either. You'd see a similar picture if you looked at any other economically relevant interest rate. In general, as my friend Hasan Comert shows in his just-defended dissertation, the Fed lost control of the important interest rates some time ago. So the best thing you can say for the zero lower bound, is that arriving there has dramatized a truth that should have been evident for some time already.
As usual, Keynes got it right: "The acuteness and the peculiarity of our contemporary problem arises out of the possibility that the average rate of interest which will allow a reasonable average level of employment is one so unacceptable to wealth-owners that it cannot be readily established merely by manipulating the quantity of money. ... The most stable, and the least easily shifted, element in our contemporary economy has been hitherto, and may prove to be in future, the minimum rate of interest acceptable to the generality of wealth-owners." The failure of interest rates to move to a level compatible with full employment is not a technical problem, but a structural one.