Or at least, that is one logical interpretation of this chart, which measures income inequality before and after taxes and benefits in advanced countries (the chart is from an OECD report on inequality). The difference between the blue and grey bars for each country is a rough measure of how much the government intervenes to make household disposable income more equal than the 'market' allocation.
Two things stand out here.
First, all governments reduce inequality, but they vary a lot in terms of how much they intervene to change pre-tax allocations. Belgium has pre-tax inequality at a similar level to Canada, but post-tax inequality is much lower in Belgium. Pre-tax inequality in Italy is even higher than in the US, but post-tax it is much lower. So governments can do quite a lot to make society less unequal, at least in terms of income.
Second, on a rough measure of how these different countries have performed in the years since the current downturn began, high levels of redistribution seem to correlate with better outcomes. So, Sweden, Denmark and Finland, who have low deficits, trade surpluses and have recovered lost output more quickly, also happen to have a much greater difference between pre- and post-tax income inequality. In other words, they redistribute more. Even Germany, although it has intermediate levels of inequality, redistributes almost as much as the Nordics. The basket cases: the US, the UK and the GIIPS countries, are all at the low redistribution end of the scale, and have suffered bigger losses of output, and bigger fiscal deficits (and this is probably not endogenous, given the data come in part from the pre-crisis period).
So the best predictor of emerging quickly from the world's worst recession for 80 years is to have high taxes, high public spending, and substantial reallocation of market income from rich to poor.