Budgets do not come from the White House. They come from Congress and the party that controlled Congress since January 2007 is the Democratic Party.
Furthermore, the Democrats controlled the budget process for 2008 & 2009 as well as 2010 & 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 2009 though, Nancy Pelosi & 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 2009 budget.