For all the talk about the Great Depression, we are missing one historical analogy for a program of large fiscal stimulus, namely Germany after the Berlin Wall came down. The two countries united, lots of money was spent and lots of money was borrowed. West Germany had a modern economy with both manufacturing and services. At the time Germany had unemployed resources, especially if you count the labor moving from East Germany to West Germany as grossly underemployed and available for higher-return projects.
The results were less than wonderful. The higher demand boosted measured gdp growth in the short run (bananas and porn, plus reconstruction) but Germany fell into economic stagnation. The new demands took the West German economy only so far. The higher taxes and debt then kept the German economy down for many years. Few Germans were happy with the economic fallout from this "stimulus." And that was with a relatively well-functioning financial system and a reasonable amount of initial optimism.
You can list many dissimilarities between German unification and the current U.S. situation (and in the comments I am sure you will). Still, as historical examples go, I believe this one has some relevance. When European leaders are skeptical about fiscal stimulus, they have some reasons, some of them quite recent.
If you'd like a lengthy account of the economics of that period, along with lots of numbers, try this study. Just read through the first few pages, you'll see statements like:
Economic theory suggests that a fiscal expansion financed by distortionary taxation could potentially generate substantial adverse growth effects after the initial positive demand stimulus dies down.
It is then estimated that the negative economic impact from the German stimulus may explain up to one third of the subsequent growth gap between Germany and comparable European nations.
Addendum: Don't be fooled by the topic-shifting comments on why East Germany didn't do better; this post is about how West Germany fared from so much stimulus. Not so great.