Paul Krugman speaks for the bears when he argues that "when everyone tries to pay down debt at the same time, the result is a depressed economy and falling inflation, which cause the ratio of debt to income to rise if anything." I think his logic is flawed, just as the logic is flawed behind the assumption that an increase in outstanding debt leads to an increase in total demand.
The fallacy here is that borrowing increases demand, while deleveraging reduces demand. It's simply not true, except in the case that the lender happens to be a bank that is using its reserves to increase the money supply. Even then, an increase in the money supply cannot result in a real increase in demand, otherwise we could print our way to prosperity. Dumping money into the economy only increases prices.
If A borrows $100 from B and spends the money, there has been no increase in demand because B now has less money to spend. Similarly, if A repays his $100 loan to B, then A has less money to spend and B has more. When the private sector creates credit, it is not creating new money or new demand, it is only shifting money from one pocket to another. Now it's true that increased credit may result in a more efficient economy (though not necessarily), and that may result in a net increase in demand, but on the margin when one person lends to another, demand is shifted from one person to another, but no additional demand is created.
As supply-side theory tells us, new demand is created by new supply. Global demand cannot increase at all unless global production rises. Otherwise we could all get rich just by spending more, or as the late Jude Wanniski was fond of saying, "we could spend our way to prosperity." It just can't happen.
So deleveraging needn't result in a weak or depressed economy.
Mark Perry has a nice post today that is effectively a corollary to the above, recalling Milton Friedman's point that deficit spending is also powerless to stimulate an economy.