It comes from Congress, and the party that controlled Congress since January 2007 is the Democratic Party. They controlled the budget process for FY 2008 and FY 2009, as well as FY 2010 and FY 2011.
In that first year, they had to contend with George Bush, which caused them to compromise on spending, when Bush somewhat belatedly got tough on spending increases.
For FY 2009 though, Nancy Pelosi and Harry Reid bypassed George Bush entirely, passing continuing resolutions to keep government running until Barack Obama could take office. At that time, they passed a massive omnibus spending bill to complete the FY 2009 budgets.
And where was Barack Obama during this time? He was a member of that very Congress that passed all of these massive spending bills, and he signed the omnibus bill as President to complete FY 2009. Let's remember what the deficits looked like during that period and what is projected into the future to 2019 :
If the Democrats inherited any deficit, it was the FY 2007 deficit, the last of the Republican budgets.
That deficit was the lowest in five years, and the fourth straight decline in deficit spending.
After that, Democrats in Congress took control of spending, and that includes Barack Obama, who voted for the budgets. If Obama inherited anything, he inherited it from himself.
In a nutshell, what Obama is saying is “I inherited a deficit that I voted for and then I voted to expand that deficit four-fold since January 20th”.