Is there an austerity curve?

I’m intrigued by Duncan’s idea of an austerity curve. - the idea that:

cutting government spending up to a certain point leads to lower deficits but beyond a certain point, the impact of lower growth and higher unemployment means that deficits get worse as the government cuts more.

If you support the Labour party’s position of supporting small cuts but not large ones, you have to believe something like this*.
It seems to me that this is only possible if the multiplier varies with the size of cuts. For small cuts, the (negative) multiplier must be sufficiently small that GDP doesn’t fall so much that tax revenues fall and benefit spending rises by more than the initial cuts. But for larger cuts, the multiplier gets bigger, and so big austerity backfires.
To fix ideas, let’s say that a one percentage point drop in GDP leads to the deficit rising by 0.7 percentage points (pdf) of GDP. It follows that for an austerity curve to have the shape Duncan suggests, the multiplier must be less than 1.4 (1/0.7) for small cuts, but more for large ones.
I can imagine three possible reasons for this:
1. The monetary policy response. Bigger fiscal austerity requires a bigger loosening of monetary policy. But this might not work. The efficacy of quantitative easing is uncertain - partly because it works by reducing tail risk, and this varies over time. A big fiscal tightening thus increases the possibility that the monetary policy response will be inadequate, whereas a smaller fiscal tightening runs a smaller risk.
2. Labour market adjustment. With decent active labour market policies, it’s possible that a few thousand redundant public sector workers can be retrained or repositioned for private sector work. But it’s less possible to do this for hundreds of thousands of them. Greater austerity might therefore increase the mismatch between the unemployed and vacancies, thus worsening the Beveridge curve.
3. Signalling. Big austerity signals that there is a serious risk of a debt crisis. But business might take fright at this signal, and thus cut investment. More modest fiscal adjustment - a “touch on the tiller” - needn’t have such adverse signals. (I’m thinking here of a loose analogue to Caplin and Leahy’s famous paper (pdf) on monetary policy signals).
The idea of an austerity curve is, therefore, not obviously wrong - though I challenge anyone to quantify all this.
But nor is it obviously right. One could argue to the contrary, that small fiscal tightening might have bigger multiplier effects. This would happen if people think that more cuts will be needed in future, and so business investment falls as firms anticipate long years of austerity.
My point here is, I fear, merely a somewhat nihilistic and cliched one. It’s that the response of economies to macro policies varies over time and place, so that there are few stable coefficients. It is therefore simply not possible to know the precisely correct macro policies. Which makes the debate between big cutters and little cutters a little like arguments about how many angels dance on the head of a pin.
* I don’t think the alternative justification for such a position - that the economy can take small cuts but not large ones - is terribly persuasive, as it’s not obvious that it can take even small cuts.