To answer this question, David Leonhardt of the New York Times crunches the numbers (from the CBO). The self-explanatory results are in this graph (click to embiggen all the way):
The GOP is gearing up to paint the deficits as "Obama's fault". And clearly, Obama has, by his own admission, run up deficits in order to get the economy back on track. But the bleak future in terms of government debt is primarily the result of the Bush economic policies. Be on the lookout for false GOP "blame Obama" rhetoric as the months and years continue.
Leonhardt also points out that inherited or not, Obama hasn't yet provided any credible plan for reducing federal deficits in the long term. This is true, and eventually he's going to have to. The inescapable answer will includes higher taxes. Hopefully, the higher taxes will be placed on those who benefitted most under Bush's deficit-creating policies.