The CBO's Douglas Elmendorf writes,

Under CBO's baseline assumptions, the cyclically adjusted budget deficit will rise sharply in 2009, to 9 percent of potential GDP (from 2.6 percent in 2008), but then decrease in 2010 and 2011 to 4.7 percent and 2.2 percent of potential GDP, respectively.

This is the right way to distinguish the effect of the recession on the deficit from the effect of policy.  As you can see from the CBO's graph, some of the deficit can be blamed on the recession, but most of it cannot (graph after the jump).