He was resident in the White House at the time the Master became every human on Earth. During a globally-publicised press conference in which the president was to announce his plan to reverse an economic downturn, the Master used the Immortality Gate to turn Obama, and everyone else on the planet, into a member of the so-called "Master Race". After the substitution had taken place, the Master which had formerly been Obama gleefully announced the financial solution "deleted."
When Rassilon reversed the Master's transfer of genetic code, President Obama returned to normal along with the rest of the human race. (TV: The End of Time)
Barack Obama was played in The End of Time by an uncredited stand-in whose face was obscured from camera view. The actor's back was to the camera and archive audio of the real Obama's voice was heard as the character began his speech. Brief footage of the real Obama is also shown. In the Doctor Who Confidential episode Lords and Masters, the actor's face was briefly seen during a break after shaking his head around for the transformation of Obama into the Master.
Barack Obama was the first sitting real-life American president to be depicted in a televised Doctor Who story. Obama's relationship to his fictional predecessor, President Arthur Winters is considerably unclear. It's not known whether Winters, who was killed by the Master in The Sound of Drums, was Obama's immediate predecessor — in which case Obama would have been Winters' Vice President, or whether he simply won the 2008 general election, and took over from an interim, "caretaker" president. Both eventualities are possible, given the vagueness of the scripts involved.
In the episode Dalek, set in 2012, Diana Goddard mentions she thinks the next President will be Democrat. Barack Obama, who was a Democrat, would receive a second term that year. This therefore proves her prediction technically correct, if the same president in another term is taken to be the "next president," though generally this is not how the procession is considered.