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%)