I wrote my original post on this to counter the idea that the size of any increase in the deficit was at least as important as its composition, with particular reference to any fiscal expansion likely to come from Donald Trump. To put it very simply, I argued that any fiscal expansion that focused on tax cuts for the very rich and extremely dubious mechanisms designed to increase infrastructure investment should not be welcomed by those who think (as I do) there is still spare capacity in the US economy. Some subsequent helpful feedback suggests that in making this argument I should have said some things a little better.
I started my discussion with an example of how a tax cut for the rich could, in theory at least, be deflationary. The idea was that the rich would immediately consume very little of any tax cut, but if the non-rich thought that in the future their taxes might rise because of the higher deficit they might decrease current consumption. 
Talking about the rich and non-rich was very imprecise of me. I actually had in mind people who were income rich. The distinction between income and asset rich could matter, following an Econometrica paper by Kaplan and Violante that Narayana Kocherlakota pointed me to. This paper argues that there is an important group that they call the ‘hand-to-mouth wealthy’. These are asset rich individuals that hold their wealth in non-liquid form (e.g a pension), and because of the non-liquid nature of the wealth they might have a high marginal propensity to consume out of current income. It is an interesting idea with some empirical backing, but which I think only emphasises the importance of thinking about the composition of any tax cut when calculating the degree of stimulus.
In retrospect it might have been simpler to give a better known example of the potential disconnect between the aggregate deficit and a stimulus, which is the balanced budget multiplier. To the extent that fiscal policy under Trump may involve cuts in government consumption, that example could be very relevant, as Paul Krugman notes.
In the case of public investment, I again argued that the nature of this investment mattered. If the mechanism used to increase public investment (see this piece by Stiglitz for example) meant that a good proportion of this investment involved projects with a low social return (white elephants), then once again people on average would not be better off. This point depends on something which I took for granted but which I should have been spelt out: monetary offset.
Because the US economy is no longer at the zero lower bound, then an increase in GDP caused by building lots of white elephants would almost certainly lead to an increase in interest rates.  As a result, GDP might not actually increase, and useful private investment would be crowded out by useless public investment.
Once interest rates start rising from their zero lower bound, then those who argue that demand should be increased in the US (see here or here) are really complaining about monetary policy, not fiscal policy. An expansionary fiscal policy that is crowded out by the Fed might have some indirect advantages, in raising the natural interest rate for example, but the famous ‘digging holes’ argument used by Keynes no longer applies.
Once we leave the zero lower bound, tax cuts for the rich amount to a regressive redistribution of income. People should not be fooled into thinking that the tax cuts will somehow pay for themselves, through Keynesian or any other means. There is an extremely strong case for a large expansion in public investment financed by additional public borrowing, but this investment needs to go where it is needed, rather than to schemes that will generate a quick return to private sector financiers. There is a strong case for using additional demand to expand the US economy, but it will not happen as long as the Fed believes otherwise.
 I confusingly talked about the wealthy as acting as if Ricardian Equivalence held, when I should have simply said that because they were wealthy they would focus on lifetime rather than current income, and so would have a low MPC from a temporary tax cut. Assuming a tax cut for the rich is permanent is equivalent to assuming the Republicans never lose power.
 Assuming, of course, that the Fed remains independent, but Krugman argues that even if it did not we might still see higher interest rates.