If monetary policy is narrowly aimed at keeping nominal GDP on target, a reason for fiscal policy would be to prevent undesirable changes in interest rates. In particular, if deleveraging leads to a lower natural interest rate, then a budget deficit financed with T-bills would keep T-bill yields from falling. The decrease in national savings would dampen the decrease in the natural interest rate.
To show this, I described an alternative monetary regime that included no hand-to-hand currency. All payments are made with checkable deposits. The only form of base money is reserve balances-- deposits as well. Both checkable deposits and reserve balances pay interest. The interest rates paid on both reserve balances and checkable deposits change with the yields on earning assets. In particular, the interest rate the monetary authority pays on reserve balances changes with the yield on Treasury bills. The monetary authority uses ordinary open market operations to target a growth path for nominal GDP.
Consider a modification of the monetary regime. The banks can issue hand-to-hand currency on the same terms as checkable deposits. Base money still takes the form of reserve balances, but there is zero-interest hand-to-hand currency. If a bank wants to issue currency, and its depositors want it, they can withdraw it from their banks. If retailers want to accept it, they can and then deposit it along with the paper checks they receive in their own banks. The monetary authority accepts currency, along with paper checks, for deposit in reserve accounts. The monetary authority then clears the currency by debiting the reserve balances of the banks against which the currency was drawn.
Under "normal" circumstances, issuing currency is attractive to banks. A bank can hold earning assets funded by borrowing at a zero nominal interest rate.
However, if massive deleveraging pushes the natural interest rate low enough, issuing currency can become unprofitable. As a rough rule of thumb, if interest rates are so low that competitive interest rates on checkable deposits are negative, then issuing hand-to-hand currency at a zero interest rate would be unattractive to banks.
Suppose that banks cease issuing currency when it becomes unprofitable. While households who would have withdrawn and spent currency cannot do so, they will have more funds left to spend by writing checks. While those firms that specialize in making sales for currency, would be harmed, other firms will reap increased sales. There is no particular reason to believe that stopping the issue of currency would impact nominal GDP.
Of course, the disruption of the business of firms specializing in currency sales is undesirable. (On the other hand, with black market activity and tax evasion, it isn't clear that the monetary authority would be too worried about this disruption.) What is the answer? Fiscal Policy.
If the government runs a budget deficit and decreases national saving, it raises the natural interest rate. By increasing the natural interest rate, it can make the issue of hand-to-hand currency profitable for the banks, ending the disruption of the business of firms specializing in currency sales.
So, there is a rationale for fiscal policy. The government needs to run deficits to make the issue of hand-to-hand currency profitable. (Or perhaps less costly.)
In conventional monetary regimes, where the monetary authority issues hand-to-hand currency, it has a powerful incentive to request the aid of the "fiscal authority" to avoid issuing hand-to-hand currency when the expected yield on earning assets is extremely low.
When the monetary authority purchases long term or risky assets (what is sometimes treated as essential to "quantitative easing,") it is taking on risk not justified by the yield on the assets. Unfortuantely, a monetary authority can frame the problem in a different way. It can take it's obligation to issue hand-to-hand currency as an absolute, and then plead an inability to keep nominal GDP on target. Given this framing, it would claim it needs the help of the fiscal authority to maintain aggregate demand. But really, the problem is that it is unprofitable to issue hand-to-hand currency.