I would say that the deficit is at it's highest level at the early stages of a business cycle (that being after a recession and in the early stages of recovery), much like how it's at it's highest level right now. I think right now we're experiencing some very special circumstances, but you get the picture.
The reason for this is that a contracting economy causes tax receipts to decline somewhat, and because the govt is so slow at adjusting it's size and expenditures to the decrease in income, it continues to hire, spend, and act like everything is merry well into the recession. This goes on for about a year or so until the deficit gets bigger and bigger and they finally have to make adjustments. It's often not until the private sector has bottomed out that the govt finally comes to this realization and cuts spending. The thing is, because it continues to increase spending while revenues were declining, and continued to do so for a while, it often has to over-correct itself and cut spending and public jobs more than it otherwise would have if they spent within their means in the first place.
My point is that the govt and the deficit tends to lag the economic business cycle very significantly, up to two years even. They finally don't make any cuts until the new business cycle is well underway, and this often has a blunting effect on the economic recovery itself. It's often not until the business cycle reaches it's maturity stage that deficits start getting balanced out.