Some recent empirical evidence questions the typically large size of government spending multipliers when the nominal interest rate is stuck at zero, finding output multipliers of around 1 or even lower, with an upper bound of around 1.5 in some circumstances. In this paper, we use a recent estimate of the degree of substitutability between private and government consumption in an otherwise standard New Keynesian model to show that this channel significantly reduces the size of government spending multipliers obtained when the nominal interest rate is at zero. All else being equal, the relationship of substitutability makes a government spending shock crowd out private consumption while being less inflationary, thus, limiting the typically expansionary effect of the fall in the real interest rate. Subject to the nominal interest rate being constrained at zero, the model generates output multipliers ranging from 0.8 to 1.6.