Brad DeLong and Paul Krugman have a nice discussion of Liquidity Preference, Loanable Funds, and Interest Rate Spreads.
Let me add one thing to the discussion that isn't often noted, but I think is important. Consider this graph:
How might we end up in such a situation? The slope of the IS curve depends upon several parameters, and a key parameter is the interest elasticity of investment. When this elasticity falls, as you'd expect it to do in a recession, the curve becomes steeper. Thus, in a recession, as the IS curve becomes steeper, we are much more likely to end up in the situation pictured above.
Brad has a long discussion of how confidence might matter:
This is the argument of Reinhart and Rogoff: that in the aftermath of a financial crisis the economy is on the verge of a sovereign debt crisis, and fiscal consolidation is essential to avoid fear of such a sovereign debt crisis take hold--for once markets begin to fear that there might be such a crisis the fact of such a crisis is inescapable.
Brad focuses on the LM curve and the risk premium, so let me add the IS curve effects.
If the confidence effect is real, a decline in government debt would have two offsetting effects in the graph above. First, the decline in aggregate demand from the decline in debt would shift the IS curve back and make the situation worse. Second, if the reduction in debt increases confidence and makes people more willing to invest, i.e. if the interest elasticity of investment goes up due to increased confidence, then the IS curve will get flatter making things better (better here meaning that it's more likely that the equilibrium is at a positive rather than a negative interest rate -- note that the IS could also shift due to the confidence effect, not just change slope).
The backward shift that makes things worse is fairly certain, but the confidence effect is small or non-existent, at least presently. In fact, the cut in demand from the cut in the deficit could create even more pessimism and erode confidence. So the net effect on the IS curve is likely to be negative given the current state of the economy. Brad comes to the same conclusion about the LM curve effects. While it's theoretically possible that the confidence effects dominate, there's nothing in the data to suggest they do, and plenty to suggest the opposite.
One more thing this illustrates is that there are two ways for the economy to get stuck at the lower bound for interest rates. One is the traditional horizontal LM curve that Brad illustrates in his post:
That is what most people think about when they think of an economy being stuck at the lower bound. The other is the situation pictured at the beginning of the post, i.e. the intersection of the IS and LM curves is at a negative interest rate (the LM curve isn't shown, but imagine it intersecting the IS curve at the fullemployment point). Thus, the lower bound trap Brad discusses in his post isn't the same as the trap Krugman is discussing with the graph pictured above. One is about the interest elasticity of money demand and the slope of the LM curve, the other is about the interest elasticity of investment and the slope of the IS curve. These two effects are by no means mutually excusive, and I think the interest elasticity of investment component of the story is too often overlooked in these discussions. (Even when changes in the interest elasticity of investment don't result in an infeasible negative interest rate quilibrium, the changes in the slope of the IS curve have important implications for the effectiveness of monetary and fiscal policy. Fiscal policy becomes more effective because crowding out is less likely or non-existent, and monetary policy becomes less effective because it's harder for interest rate changes to cause a change in business investment).