New Keynesian macroeconomics says that a (temporary) increase in government spending will cause an increase in the natural real interest rate. And unless the central bank increases the actual real interest rate by an equal amount, the result will be an increase in Aggregate Demand, which will cause an increase in real output and/or inflation. There is a fiscal policy multiplier. Plus, if the central bank holds the nominal interest rate constant, any increase in inflation and expected inflation will cause the real interest rate to fall, which will cause an additional increase in Aggregate Demand, multiplying the original fiscal policy multiplier. (In an open economy part of the effect works through the real exchange rate.)
This sounds sensible to me. It all depends on whether or not there is monetary policy offset. (Though, strictly speaking, it also depends on what exact goods the government buys; if for example the government buys goods that are perfect substitutes for private consumption or investment, which is like the government doing your shopping for you with your credit card, fiscal policy should have no effect.)
How to test whether fiscal policy actually works as advertised by New Keynesian theory? Macroeconometrics is hard.
The biggest problem here is controlling for monetary policy; because theory says that whether or not fiscal policy works depends on how monetary policy responds to fiscal policy.