And the funny thing is? It wasn't austerity that got the US out of that depression. It was FDR's New Deal, probably still the most left-wing plan ever enacted by a US government.
Rather than 'tightening belts,' FDR responded with Social Security, the TVA, banking reform, relief funds, the housing administration, new tax policies, the list goes on.
Amusingly, even then, those on the right charged him with attacking business and even communism, but unlike the left-wing policies of the last couple of decades, he actually stuck to his guns and rode the goodwill of the people into the first and only third term in the history of the presidency.
About the only case I know of for austerity ever actually leading to anything half-good is Finland, the only country in WWII ever to pay off the full extent of its war debt. But while the eventual result was to turn the country into a proper industrial power, the intervening decades are still remembered as one of significant poverty, of literally making bread flour from tree bark because wheat was too expensive. One even wonders if this was the start of Finland's lingering reputation for depression and alcoholism, from which it is only now starting to recover.
The ugly truth about austerity politics is that it is very much about making a handful of very rich people even richer, and little else. Look at Britain, where the party of some of the richest people in the country are blabbering about tightening belts. You think David Cameron's cutting back at home?
Or hell, look at Germany. The biggest bully for austerity politics in the whole EU is also literally it's richest country. And you can damn sure bet they aren't playing the same game at home.
And oh look, just as last time Europe tried to squeeze a country into bankruptcy for its debts, there's suddenly all these new fascist parties gaining popular support, and an iron-fisted tyrant consolidating power in Russia. It's almost like we've all forgotten the 30s ever happened already ...