One of the less acknowledged of the secret sins of economists, it seems to me, is the failure to distinguish between net and gross quantities, or to treat the net numbers if they were all that mattered.
Case in point, the issue of deleveraging, where the good guys -- the anti-austerians -- are trying to get an accounting-identity argument to do more work than it it's capable of.
A good example is this post from Peter Dorman (which Krugman liked), which points out that in a closed economy one agent's debt is always another agent's asset, and total consumption must equal total income. So the only way that one agent can reduce its net liabilities is for another's to increase, just as the only way some agents can spend less than their income is for others to spend more. In this sense increased public debt is just the flipside of private-sector deleveraging; arguments that the public sector should reduce its debt along with the private sector are incoherent. QED, right?
Except, this argument proves too much. It's true that one agent's net financial position can't improve unless another's gets worse. But the same accounting logic also means that financial claims across the whole economy always sum to zero. Total net worth is always equal to the sum of tangible assets, no matter what happens on the financial side.  So it's not clear what leveraging and develeraging could even mean in these terms. So, since the words evidently do mean something, it seems they're not being used in those terms.
It seems to me that when people talk about (de)leveraging, they are almost always talking about gross financial claims, not net, relative to income. A unit that adds $1,000 in debt and acquires a financial asset valued at $1,000 is more leveraged than it was before. And in this gross sense, it is perfectly possible for the public and private sector to simultaneously deleverage.
Consider the following very simple economy, with just two agents:
The transition from T1 to T2 involves simultaneous deleveraging -- in the economically meaningful sense -- by both the agents in the economy, and no national accounting identities are violated.
What would this look like in practice? To some extent, it could simply mean netting out offsetting financial claims, but that only really works within the financial sector; nonfinancial actors don't generally hold financial assets and liabilities at the same time without some good institutional reason. (A firm may both receive and extend trade credit, but those two lines on the balance sheet can't be netted out unless we want to go back to a cash-on-the-barrelhead economy. A typical middle-class household has both retirement savings and a mortgage and student-loan debt; both the borrowing and saving are sufficiently subsidized and tax-favored that it makes sense to add to the IRA rather than paying off the debt. ) To the extent that this kind of deleveraging does take place within the nonfinancial sector, it requires that units reduce their gross saving, i.e. their acquisition of financial assets -- a suggestion that will seem even more paradoxical to conventional wisdom than the claim that private-sector deleveraging requires increased public debt.  But there's another approach.
Most borrowing by households and nonfinancial firms and households is undertaken to finance the acquisition of a tangible asset -- in the table above, we should really divide the assets column into tangible assets and financial assets. For the low net worth units, most assets are tangible; for middle-class households, the house is by far the biggest asset, while property, plant and equipment is generally the biggest item on the asset side of a nonfinancial firm's balance sheet. So the most natural way for the private sector and the public sector to deleverage is through a transfer of tangible assets from debtor to creditor units, combined with the extinction of the debts associated with the assets. This is, in essence, what privatization of public assets is supposed to do, when the IMF imposes it as part of a structural adjustment program. And more to the point, it's what the foreclosure process, in its herky-jerky way, is doing in the housing market. At the end of the road, there's a lot less mortgage debt -- and a lot more big suburban landlords.  And the private sector has reduced its leverage, without any increase in the public sector's.
(Of course, we could just extinguish the debt and skip the asset-transfer part. But that default could be a means of deleveraging is one of those thoughts you're not allowed to have.)
Now, all this said, I completely agree with Dorman's conclusion, that reducing public debt would hinder rather than help deleveraging. (Or rather, what he thinks is his conclusion; the real logic of his argument is that nothing can help or hinder deleveraging, since -- like motion -- it does not exist.) But the reason has nothing to do with balance sheets. It is because I believe that fiscal consolidation will reduce aggregate income -- the denominator in leverage. I reckon Dorman (and Krugman) would agree. But this an empirical claim, not one that can be deduced from national accounting identities.
 Or the sum of tangible assets and base money, if you don't treat the latter as a liability of the government. This is a question that gets people remarkably worked up, but it's not important to this argument. (Or to any other, as far as I can tell.)
 Actually I suspect many middle-class households are saving more than is rational -- they're acquiring financial assets when paying down debt would have a higher return. But anyone who knows me knows how comically unsuited I am to have opinions on anyone else's personal finances.
 Reducing debt and and expenditure simultaneously doesn't help, since one unit's expenditure is another's income. For financial deleveraging to work, people really do have to save less.
 Who might or might not end up being the banks themselves.