Suppose Obama is elected in November.
Then suppose that a SCotUS justice dies or retires in December.
Will (lame duck) Bush or incumbent (and Democrat) Obama have the right to appoint their replacement?
Moot point. Bush is still Prez, so it goes to him. But Congress would just stall until after Jan. 20. In fact, as near as I can read their schedule, Congress won’t even be in session until Jan. 15.
Bush would have the right to try. He’s in full power until he’s gone. But I think the Senate would be unlikely to move swiftly on the nomination. He could try a recess appointment, but I think that would be unlikely too.
Even if he did the justice would only serve less than a month before his appointment expired.
SCOTUS appointments don’t “expire.”
Recess appointments do.
But it should be noted that they expire not when the new President shows up, but when the next session of Congress (specifically, the Senate) comes to a conclusion. Thus, the recess appointment usually lasts about a year.
Amplifying Antinor’s point:
For any appointment for which the President’s nominee would require confirmation by the Senate, an appointment made without the Senate’s advice and consent while they are in recess is valid only until (a) confirmed by the Senate when it reconvenes, (b) the nomination and confirmation of a replacement, or (c) the end of the current Senate session, whichever comes first. It doesn’t matter if the nominated-and-confirmed normal appointment’s term is for good behavior, a fixed number of years, or at the pleasure of the President; the above holds for any recess appointment. Cite: Somewhere in the Constitution, I think Senate powers in Article I.
Article II, Section 2 if you want to be precise.