The longest confirmation in history was apparently Brandeis at 125 days. Assuming Obama takes about a month to get a nomination together that leaves just over 300+ days left in this administration. That said, would not surprise me to see the Senate serially find reasons to reject say 3-4 candidates or screw precedent and just take forever to run out the clock on purpose.

They will likely also have pro forma sessions to deny a recess appointment as well [1].

[1] https://en.wikipedia.org/wiki/NLRB_v._Noel_Canning

One option Obama would have that might fill the seat before his term is up is to go back to providing a real list of a number of candidates instead of the "list of one". The chance of this happening is near zero of course; I guess he'll nominate someone a bit closer to the center and let them be stonewalled, something which may help the democrats in the election.

I imagine a lot of good candidates, knowing the nomination is destined for limbo, might opt out of the media circus and decline it.

Of course if the Dems win the election the incentive to stall fades considerably.