Can a large-scale deficit spending program speed up recovery after recession? To answer that question we calibrate a standard neoclassical growth model with US data and assume that an exogenous shock has driven aggregate output far below steady-state and that the economy is expected to recover very slowly. We calibrate the model such that a permanent increase of government expenditure is effective in raising output (with a multiplier of 0.75 in the benchmark case). We then show that a "fiscal stimulus", i.e. a temporary increase of government expenditure is not only ineffective but detrimental. Even before the spending program expires, aggregate output is lower than it could be without fiscal stimulus. We show the generality of this result w.r.t. size and persistence of the shock, size of the government multiplier, and the scale and duration of the stimulus program. A phase diagram analysis provides the economic intuition for our unpleasant finding and explains why, generally, private capital stock reaches its lowest level when a fiscal stimulus program expires.