What did Obama do in meantime? I actually think he would have retired from the senate in 2010 and run for governor instead as never liked being a senator. Remember that Blago would have remained in office for the rest of his term. Although Illinois doesn't have term limits, I could easily imagine a scenario in which leaves it to Obama, perhaps seeking to switch jobs. Obama would certainly not have been vice president, if anything in Hillary's administration, it's Attorney General.
I absolutely a gifted campaigner like Obama would have defeated Trump. Kaine is still a likely running mate. Obama strongly considered him in 2008. Joe Biden would have been considered too old. I think he may have been Secretary of State after 2009.
✓ Governor Barack H. Obama (D-IL)/Senator Timothy M. Kaine (D-VA): 323 EV. (51.03%)
Mr. Donald J. Trump (R-NY)/Governor Michael R. Pence (R-IN): 215 EV. (45.83%)
This in most cases. I don't think Obama runs for Governor in 2010 if he just ran for President in 2008 and lost the nomination. He's almost certainly not holding any position in Hillary's administration. Modern day teams of rivals and unity tickets just don't work. In real life, Hillary was not going to accept Secretary of State initially. Looking back, that was probably a mistake for her to accept the position.
Biden likely becomes Secretary of State in 2010/2011 after Richard Holbrooke dies, who probably would have been Hillary's Secretary of State in real life.