Let's start at the beginning. Depressions are caused by a slight increase in people's preference to hold onto cash, which causes a downward spiral where the economy slows and then people want to hold onto cash more.
The first thing you try to do in this instance is increase the money supply, but we've gone as far as we can go on that -- the Fed has sent the interest rate to zero and it can't go any lower.
So, as Keynes said, the second thing you try to do in that scenario is let government spending pick up the slack and take advantage of the productive capacity that isn't being used on anything to get the economy moving again.
Greenspun claims this won't work because "a lot more globalized today and there is much more competition among countries." First, we've only recently caught up to the levels of international integration we had during the first wave of globalization, starting in 1870. Second, countries don't compete with each other. The fundamental well-being of a country is determined by simply its domestic productivity. What would we be competing for?
He seems to suggest that we're competing for international investment dollars. But then why do you think government investment won't work? Why is international investment this magical thing we must attract to start businesses?
He claims that Japan's huge fiscal stimulus proves stimulus doesn't work. But in Japan, stimulus did work -- when it was tried. As the leading scholar wrote: "the 1995 stimulus package ... did result in solid growth in 1996, demonstrating that fiscal policy does work when it is tried. As on earlier occasions in the 1990s, however, the positive response to fiscal stimulus was undercut by fiscal contraction in 1996 and 1997."
See http://mediamatters.org/items/200812220005 for more.