Well I don't think she will be there for that many to be heard in the short term but there are a couple key issues coming up before the end of the year.
More interesting is how is this going to be done.
Certainly she would follow through and issue her opinion on the cases for which she heard arguments, and she would simply stop attending arguments for new cases after Alito joins the court.
But does that mean there will be a period of time for which we have 10 judges? Could someone object that the Supreme Court accepted the case, and therefore they should be heard by ALL the Judges?
Sometimes these judges issue injunctions, and what-not separate from the whole court. Are there 10 such injunction sources for that period?
What if some other judge shuffles off this mortal coil before O'Conner wanders off to retirement? Do we hold her over?
The court has had as many as 18 (i think) judges in the past, but there would be a lot of potential for mischief.
Alito can't vote on any cases where he wasn't there for the arguments and O'Conner's vote doesn't count if the vote is handed down after she has left even if she has heard the arguments. There can never be 10 judges on the supreme court. You need 6 judges for a quorum and the most judges there can be are 9.