On the left
The point of disagreement is disguised as being a disagreement over the Keynesian multiplier: is it 1, is it less than 1, is it greater than 1 (recall the multiplier is simply the effect of a $1 cut or increase in spending on GDP)....
But really, economists' views on the multiplier have almost nothing to do with scientific inquiry and have almost everything to do with where they lie on the political spectrum. Mankiw, being a Republican thinks the multiplier is small (big surprise) and that therefore the cuts won't hurt GDP or employment much. Goolsbee (for example) being a Democrat thinks the multiplier is bigger - and that the cuts may in fact take a noticeable chunk out of GDP and employment.
The point is, all these economists pretend their differences are a matter of math and science, when they really are almost soley a difference of politics.
[Not to mention that both sides are ignoring that the Keynesian multiplier says nothing about employment - it only says what the effect of spending cuts on GDP is. To the degree that GDP and employment are not 100% correlated (which of course they aren't), the multiplier itself says very little about employment.]
From Keynes' General Theory, Chapter 20:
"It follows from this that the assumption upon which we have worked hitherto, that changes in employment depend solely on changes in aggregate effective demand ... is no better than a first approximation, if we admit that there is more than one way in which an increase of income can be spent."