We have the increase in federal debt to nominal gdp (red) and the increase in nominal gdp (blue). The change in GDP was 16 points during the period from 2008 to June 2013, The total nominal GDP increased by 16 index points.
The change in debt to GDP was 60 index points, so the economy changed 16 index points to the government 60. The government spending changed 60 from a starting point of 100, the total economy changed 16 from the starting point. A multiplier of 16/60 says each increase in government spending associates with an increase in total spending of .26.
If DC were balanced, then the private sector and DC should grow together, by the same percentage. That is, both DC and the private sector should be responding equally to the external shock, positive or negative.
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