Before Mr. Obama takes office on the 21st of January, Iraq is going to go through a fair bit of wrapping up. As the DoD map below shows, all but Baghdad (18 of 19 provinces) will have been transitioned to full Iraqi control soon: according to the DoD September Report to Congress, the ceremonies will all happen in early and mid-Jaunary. Baghdad's ceremony will be in May--though it should be noted that its ceremony has been continually pushed back from October 2008.
With Iraqi Security Forces at the front in all of these provinces, Petraeus is likely trying to train them by fire--US forces will be in the back (notably, taking far fewer casualties than when in the front) provoding logistical support and giving advice. This "school for hard-knocks" is going to get Iraqi forces pretty chewed up over the next few months, but it will mean high-speed learning. So far, only a small percentage of Iraqi military forces are capable of full independent operations--logistics, supply, planning, and execution. Most need planning help from the US. Many need US logistics or even military backup. They must wean this dependence by 2011, or they will falter when the US withdraws.
Another reason for the speedy handover is the terms of the Status of Forces Agreement (SoFA). While US forces don't leave until 2011, they have to get off the streets of Iraqi cities and villages by the end of 2009--during 2010 and 2011, US forces can only act at the behest of the Iraqi government. They will continue to train, but will only get militarily involved when the Iraqis need the cavalry to come in.
The handover involves more than military control. It also signals full administrative control on the part of the Iraqis, with the State Department playing a purely supportive role. With Gates remaining head of the DoD and Petraeus keeping his post as head of CENTCOM, Bush appointees will be at the forefront of Iraq's endgame through 2011 (barring anything strange). Obama and Clinton will have surprisingly little influence over the Iraq situation, as policies being made now (namely the SoFA and handover timetables) have mostly sealed any questions on the remaining US role. This will free up the "team of rivals" to deal with more pressing crises--Afghanistan, Pakistan, and India are the main points of worry.