Fiscal stimulus and Investments

Is public spending going to crowd-out private investments?
That sounds like a Macro 1 question, something like IS-LM textbook model...

Eugene Fama argues that "The added debt absorbs savings that would otherwise go to private investment. In the end, despite the existence of idle resources, bailouts and stimulus plans do not add to current resources in use. They just move resources from one use to another." and "The new government debt absorbs private and corporate savings, which means private investment goes down by the same amount." 

John Cochrane says "If the government borrows a dollar from you, that is a dollar that you do not spend, or that you do not lend to a company to spend on new investment. Every dollar of increased government spending must correspond to one less dollar of private spending."

Basically they start from the national accounting identity S+T=I+G (let's omit open economy for simplicity) and claim that one more dollar to G is one less dollar to I, like if all the rest of the economy, in particular S, were super-fixed.

Brad DeLong and Paul Krugman do not agree. You may say they are keynesians, but still saying that so many things in the economy are fixed seems quite a strong assertion to me. They make two different points one about the money market and one about the goods market.

DeLong makes an easy example of a credit economy in which, given the money stock, we can get higher output or just nothing depending on how people behave. The point is that there is unemployment and the velocity of circulation of money can change: "Cochrane's mistake--an elementary, freshman mistake--is because he has not thought enough about how a credit economy works to recognize that the velocity of circulation can be an economic variable and is not necessarily a technological constant. And as the velocity of circulation varies, the amount of the flow of spending varies as well." 
Without the need of helicopter money, a fiscal stimulus can thus incentivate people to put their money into circulation through the credit system, which leads to higher output.
This works unless you believe that velocity of money is given, that spending is given unless new money is printed and that the economy is always at its best...

Krugman says "after a change in desired savings or investment something happens to make the accounting identity hold. And if interest rates are fixed, what happens is that GDP changes to make S and I equal." 
He underlines that S+T=I+G is just an accounting identity. That is at the end of the day it must be true, but it says nothing on how things change and respond to one another. Actually if G is increased, GDP might go up, leading to higher S and T, without necessarily crowding-out private investments.
Again, this works unless you believe that GDP is given, S is given etc.

I don't want to argue in favor to one or the other, but that was all in the basic undergraduate IS-LM model. So once again do you believe money is affected by interest rates? Are we in a liquidity trap?