Budgets do not come from the White House. They come from Congress – each for a “fiscal year” which begins on October 1 and runs until September 30 of the next year.
The party that controlled Congress since January 2007 was the Democratic Party. It controlled the budgets for fiscal years 2008, 2009, 2010, and 2011.
In their first year in control of Congress, 2007, they had to contend with George Bush for the 2008 budget, which caused them to compromise on spending, leading to a $458 billion deficit. However, for 2009 Nancy Pelosi and Harry Reid bypassed George Bush entirely, passing continuing resolutions instead of a budget, keeping government running until Barack Obama could take office. Then they passed a massive omnibus spending bill to complete the fiscal 2009 budget.
And where was Barack Obama during this time? He was a member of that very Congress that passed massive spending bills for fiscal 2008-2009. He then later signed the omnibus bill, as President, to complete fiscal 2009.
If the Democrats inherited any deficit, it was the fiscal 2007 deficit, the last of the Bush-Republican-Congress budgets. That deficit was the lowest in five years, $160 billion, and the fourth straight annual decline in deficit spending.
After fiscal 2007, Democrats in Congress took control of spending – and that included Barack Obama in the Senate 2007-2008, who voted for these budgets.
If Obama inherited any deficits, he inherited them from himself. In a nutshell, what Obama is saying is "I inherited a deficit that I voted for and then I expanded the average annual deficit four-fold since I became President."
http://www.usgovernmentspending.com/spending_chart_2002_2012USb_13s1li111mcn_G0f for the actual numbers instead of the chart.