The Congressional Budget Office defines the federal budget deficits (pdf) as when spending exceeds revenues for the fiscal year (October 1st through September 30th) so it is reasonable to assume that this what President Obama is referring to when he maid that claim. Additionally, since the deficit is defined solely on the basis of the receipts vs. outlays, programs such as the Troubled Asset Relief Program (TARP) are included in the official figures.
According to the Monthly Treasury Statement for September 2013 (pdf) there was a $680 billion deficit for Fiscal Year 2013 through September 30, 2013. According to the Office of Management and Budget Historical Tables, the following are the total receipts, outlays, and deficits for 2008 through 2012 (source, xls) in nominal dollars:
Year Receipts Outlays Surplus or Deficit (-)
2008 2,523,991 2,982,544 -458,553
2009 2,104,989 3,517,677 -1,412,688
2010 2,162,706 3,457,079 -1,294,373
2011 2,303,466 3,603,059 -1,299,593
2012 2,450,164 3,537,127 -1,086,963
Using the Fiscal Year 2009 deficit of $1,412 billion that means that as of August 2013 the Fiscal Year 2013 reduction of $680 billion is accurate on the hard numbers and is about a 52% reduction.
If we adjust these values for inflation by using an inflation calculator then we find that $680 billion in 2013 dollars is the same about $623 billion in 2009 dollars. This represents about a 56% reduction in the deficit when compared to it in 2009 which means that the statement is also accurate using inflation adjusted figures.
Another way of looking at the deficit is as a percentage of the gross domestic product (GDP) which has also been done by President Obama and was examined by FactCheck.org,
In fact, although the White House didn’t cite it, the newly released
mid-year projection from the White House Office of Management and
Budget for the 2013 fiscal year shows that due to rising revenues, the
2013 deficit is now projected to be $759 billion — $214 billion lower
than the $973 billion deficit projected in the original budget. As a
percentage of GDP, the 2013 deficit is now projected to equal 4.7
percent. The nonpartisan Congressional Budget Office projects an even
lower 2013 deficit of $642 billion, or 4 percent of GDP. That’s still
above the level in 2008 (or any year since 1992), but it’s
substantially lower than 2009. (Even if those projections pan out,
however, Obama’s talking point wouldn’t be correct.)
where the deficit as a percentage of the GDP was -10.10% on December 31, 2009 which would make this claim accurate but still dependent upon the final Fiscal Year 2013 data.