Seems like it usually takes a month or two for presidents to appoint someone new, and this might be affected by the supreme court's schedule, too.
The game theory of this is interesting, for instance, what if Obama nominates someone that is seen as more moderate than someone that Hillary or Sanders would nominate?
I will be shocked if Hillary nomination is more liberal than Obama's. Hillary is a conservative in Democrats clothing currently she is spouting liberal agenda to get the nomination once elected whe will go for conservative options under the umbrella of getting things done.
Hillary, in my opinion, is whatever she needs to be to get her way. My biggest concern with Hillary is that in order to win the high office, she'll have to embrace the progressive mantle. If so, her first appointment would likely be one that leans progressive, if only to ensure that she keeps the peace enough to be re-elected to a second term.
The game theory of this is interesting, for instance, what if Obama nominates someone that is seen as more moderate than someone that Hillary or Sanders would nominate?