Krugman posted a 1998 paper here., which goes some way to explaining what he might be thinking about here. The 1998 Krugman and I apparently think alike. The example he used in his paper is exactly the same one I used here. If anyone doubts the existence of liquidity traps, it is clear that we can produce these in essentially any mainstream, precise, dynamic general equilibrium monetary model. The liquidity trap that Krugman produces is one where you fix monetary policy in the future, ask what it takes in terms of monetary policy to drive the nominal interest rate to zero in the present, then ask what happens if you go further. Once the nominal interest rate is at zero in the present, if the central bank injects more money at the margin, this is irrelevant. In an earlier version of a paper I am currently revising, I included an example that looked almost identical, in a Lagos-Wright construct, but you can do the same with cash-in-advance, as Krugman does. Krugman's 1998 paper then gets into some hand-waving about insufficient demand, real interest rates that are too low (he's describing Japan at the time), etc., that I did not find so useful, but we'll leave that aside for now.
Krugman's 1998 example, which is a temporary liquidity trap, works in exactly the same fashion as phenomena that occur in essentially all monetary models at the Friedman rule. The Friedman rule is a rule for monetary policy that implies a zero nominal interest rate forever. At the Friedman rule, there is always a liquidity trap. Another way to think of this is that there are many paths for the money stock that are consistent with having a zero nominal interest rate forever. If, for example, negative money growth of -4% per year with an initial money stock M implies that the nominal interest rate is zero forever, then -4% per year money growth with an initial money stock xM also implies the nominal interest rate is zero forever, where x > 1. Further, the path for price level in the first case is also an equilibrium in the second case. Note that this is not just standard neutrality of money as the quantities and the prices are the same in both cases. However, it's not any money stock path that will support the Friedman rule. What Ricardo Lagos shows here (and this is related to work done long ago by Charles Wilson) is that, roughly, the money stock has to go to zero in the limit. This is all about the long run, and the forward looking behavior of economic agents. If we do not anticipate that the money stock will be decreasing at a sufficient rate indefinitely, this cannot happen.
Now, Krugman and others seem to associate liquidity traps with deflation. That is certainly the standard Friedman-rule logic, and it could be that when Krugman says "deflation trap" he means "liquidity trap." In the paper I'm revising (see these slides) you can show that liquidity traps can occur for any inflation rate, with monetary policy set appropriately, and the trap can persist forever. The liquidity trap arises in taking full account of the role of banks. What happens is that, if private assets used in financial exchange are sufficiently scarce (e.g. in a financial crisis), and cash is sufficiently plentiful, then the nominal interest rate can be zero, potentially even with a positive rate of inflation. There is nothing particularly weird going on here - no funny equilibria or disequilibria.
Note that there are other liquidity trap phenomena, related to current policy. For example, under current conditions with a positive level of excess reserves, and interest paid on those reserves, a swap by the central bank of reserves for T-bills is essentially irrelevant, for the same reasons you get a standard liquidity trap. The central bank is just swapping one interest bearing asset for another that is essentially identical.
What's the bottom line? First, the conditions required to support sustained deflation in standard models seem hard to fulfill in practice given what we understand about commitment by the Fed to future policy. Second, it is possible to have a sustained liquidity trap without sustained deflation. These are just more reasons why we should not be too worried about deflation.