The President doesn’t control the economy, and should not be blamed for things out of their control. The deficit is however one the components of the economy where the president has lots of direct control. Even this controll is far from complete, presidents can be lucky or unlucky. For instance the deficit declined during the 1990s IT-boom when Clinton was president and was increasing rapidly when Obama took over following the 2008 crash, in both cases having little to do with their actions.
Though the debt numbers alone do not tell how much credit or blame the president deserves, they are interesting. Data from The White House 2012 President's Budget. Since the figure is for the end of the year and the President takes office one month into the year, they correspond well with tenure.
During 20 years of the presidencies of Reagan, Bush I and Bush II, the federal debt as a share of GDP increased by a cumulative 43% of GDP. During the 4 first years of the Obama presidency, it has increased by 36% of GDP.
This is how the Presidents rank in terms of development of the Debt/GDP ratio per year of tenure:
1. Clinton -1% per year
2. Reagan, Bush II: +2% per year
3. Bush I: +3% per year
4. Obama: +9% per year.