If I were a different sort of person, I would now be accusing some macroeconomists of deliberately misrepresenting the policy implications of their models in order to further their own political agenda.
But I am not that sort of person. I don't generally go for conspiracy theories. And I myself used to make the same mistake that they are now making. Because I didn't understand that model properly. So I figure it's very likely the simple explanation: they don't understand it properly either. But it would be prudent for them to avoid throwing stones.
It's important that we do try to understand our own models properly, so we can try to teach them properly. And at least try to present the policy recommendations of our models without spin. Subject to all our usual human imperfections, of course. And if we don't like those policy recommendations, that's OK too. That should lead us to re-examine our models.
Let G(t) be the level of government spending at time t. Let Gdot(t) be the derivative of G(t) with respect to time. Let r*(t) be the natural rate of interest at time t.
In Old Keynesian models, with an Old Keynesian IS curve, r*(t) is a positive function of G(t) and is independent of Gdot(t).
In New Keynesian models, with a New Keynesian IS curve, r*(t) is a negative function of Gdot(t) and is independent of G(t).
Any good New Keynesian macroeconomist will be able to understand why that is true, but may not have thought about it that way before. In a simple model where C(t)+G(t)=Y(t), where Cdot(t) is a positive function of r(t) by the consumption-Euler equation, and r*(t) is defined as the time path for r(t) such that Y(t) equals potential output Y*(t) for all t, so Cdot(r*(t))+Gdot(t)=Y*dot(t), that's what you get. But they can do the math much better than I can.
Suppose the economy is stuck at the ZLB at time t, and we want fiscal policy to increase r*(t).
The Old Keynesian policy recommendation is to increase G(t).
The New Keynesian policy recommendation is to decrease Gdot(t).
Those are very different policy recommendations. We have slipped one derivative, and changed the sign.
In a discrete time model it is harder to see the difference. Because if we increase G(t) and leave G(t+1) unchanged, we decrease (G(t+1)-G(t)). But if we decrease G(t+1) and leave G(t) unchanged, we also decrease (G(t+1)-G(t)). [Update: two math/typos fixed. Well-spotted primedprimate!] According to the New Keynesian model, both will work equally well in raising r*(t).
I have heard macroeconomists recommend increasing G(t) temporarily, and saying that the New Keynesian model supports this policy recommendation.
I have never heard a single macroeconomist recommend reducing Gdot(t), and saying that the New Keynesian model supports this policy recommendation.
If a policymaker said "We need to start cutting government spending now, and keep cutting until the economy is off the ZLB", would any macroeconomist say that the New Keynesian model supports that policy? Because it does.
If we also recognise that G(t) is not in practice a jump variable, that can be made to jump right now, and that fiscal policy changes take time, and so Gdot(t) is the more realistic control variable, then this inconsistency between what macroeconomists recommend and what the New Keynesian model recommends is even more glaring. Announcing that G(t) will be slowly falling from now on until the economy is off the ZLB works equally well, according to the model, whether or not it is accompanied by an instantaneous jump in G(t). But an instantaneous jump in G(t) is hard to implement unless you have planned it well before time t.
If you think that cutting Gdot(t) at the ZLB won't work, that's OK. But don't use the New Keynesian model to support raising G(t) at the ZLB. Because the New Keynesian model says that raising G(t) only works if and because it means cutting Gdot(t). It says that raising G(t) is just a sugar cube to help the cutting Gdot(t) medicine go down. [Update: not that there's anything wrong with taking the sugar cube, but it is wrong to say the New Keynesian model says the sugar cube is what cures you.]