Well, we all know that recessions are caused by imperfect information in the market (though not all GDP decline is necessarily a recession as we usually use the term. For example, WWII France).
The economy misallocates its resources, often as the result of a speculative bubble, wherein resources are invested with the knowledge that the investment's fundamentals may be sound. When the bubble ends and some group of investors is standing around confusedly like the loser in a game of musical chairs, the economy must correct itself and liquidate a good chunk of the unsound industry. Layoffs and bankruptcies ensue, which ripple through the economy and other industries lose jobs temporarily as a secondary effect.
Better information and credit would eliminate these side effects, but they don't exist. Credit is actually worse during a recession.
The exception is government spending like teachers, Medicare, and military. While the rest of the economy is shrinking and wriggling to readjust, government programs continue blithely along. This may seem helpful at first glance, since they don't suffer the unnecessary adjustments that some other industries do.
However, the result is that the percentage of spending on government services actually increases. While businesses are cutting employees, inventory, hours, profits, and investment, their taxes + monetary inflation stay the same. Reducing (taxes + inflation) proportionately over the course of the recession would help. That's actually similar to what the Keynesians recommend.
The problem is that any decrease in taxes without an equal decrease in spending increases the deficit. Bonds are issued, the monetary supply inflates, and the result is that inflation costs the public as much as the taxes did.
Unfortunately, it will be decades before economists bother to prove this idea one way or another: that government spending and taxation should be cut proportionate to GDP declines in recessions.