It’s understandable that as we face a shock comparable in magnitude to the Great Depression, there will be a push to look at the policy responses of that period as a guide for current action. That's why it's to get that interpretation straight. In the case of Nazi Germany, commentators like Brad DeLong have emphasized how Hitler’s Keynesian policies brought the country out of Depression.
This interpretation is misleading, as laid out by Adam Tooze in his wonderful book on Nazi economic policy, The Wages of Destruction. As Tooze shows; Germany did, indeed, recover from the Great Depression while under Nazi rule. But the nature of that recovery was not particularly “Kenynesian” as we understand the term today; and offers a limited guide for current policy.
The impact of Nazi make-work schemes and infrastructure building has been drastically overstated—including by Nazis themselves. While these schemes served as great propaganda pieces, they competed with funding with the Nazi military buildup. As Nazi Germany faced competing demands between guns and butter, it systematically chose to prioritize military spending while downplaying civilian consumption.
The impact, too, of these programs on unemployment was limited. Even by the 1930s, technology improvements were already lowering the need for unskilled workers at construction sites. Fiscal stimulus may have had an effect on reducing unemployment in backward regions, like East Prussia, but was of more limited use in the more developed regions of Germany. Tooze documents that unemployment changed relatively little in urban areas during the early recovery period. Even autobahn construction required relatively few workers--under 40,000 a full year after construction began. At their peak, make-work schemes constituted a minority of all employment. Of course, infrastructure construction today is even less intensive in workers today, and a stimulus might be even less effective.
The systematic effects of Germany’s prioritization of military aims led to devastating outcomes for German consumers. Remember; Keynesian stimulus is generally advocated out of the idea that we need to increase consumption today. German economic recovery was actually ongoing as Hitler gained power--but household consumption was then sharply curtailed in order to boost military spending. Private demand accounted for less than half of the growth in aggregate demand from 1933-1934. Germany's economy had recovered in 1935 to the level it had been in 1928--a marginally better performance than America. Yet private consumption and investment were below pre-Depression levels, while state spending was 70 percent higher, led by the military.
Perhaps one could argue that though the aim of Nazi Germany’s stimulus was misdirected towards the armed forced; it still had net effects on economic growth. A different policy which matched the Nazi drive for stimulus, but which redirected it towards public goods, may have worked equally well without the war side effects.
Perhaps—though Tooze cautions us on this score as well. The reality is that many different governments, each following different economic policies, ultimately recovered from the Great Depression. It is impossible to know the counterfactual policy—but scholars such as Barry Eichengreen and Christina Romer have convincing work that suggests that monetary boosts, in the form of exiting the Gold Standard, formed the primary basis for international economic recovery.
This is not to say that further fiscal stimulus now would be a bad idea. But the lessons of 1930s Germany are not exactly an ironclad defense of the wisdom of spending your way to prosperity.