If it weren't for the Zero Lower Bound on nominal interest rates, there would be no macroeconomic role for fiscal policy in New Keynesian models. Monetary policy alone could and therefore should be used to hit the macroeconomic target, because this leaves fiscal policy free to try to hit its many microeconomic targets as best it can. (There are perfectly good microeconomic reasons why fiscal policy should be countercyclical, but that's another story.)
But if a big drop in demand causes the natural rate of interest to fall too low, relative to the inflation target, the ZLB maybe be a binding constraint on monetary policy in New Keynesian models, because the central bank cannot drop the actual real rate of interest down to the natural rate. So you might want a countercyclical fiscal policy, that raises the natural rate when private demand is low and the natural rate is low, and lowers the natural rate when private demand is high and the natural rate is high, to keep the economy away from the ZLB. Let's assume you do.
What would you need to do to government spending in a New Keynesian model to raise or lower the natural rate of interest, and to mitigate those fluctuations in the natural rate? The answer is not what you probably think it is.