If Christie wants to run in 2016, that will dictate his pick.
Months? I don't think NJ has special elections, the appointment will last for 2 years (though I could be wrong).
The law is ambiguous. Democrats want a 2013 special. Christie is presumed to want no special because Booker being on the ballot for senator could boost Democratic turnout in the gubernatorial race too.
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EDIT: I just voted in this poll that Christie picks an Independent but without that option I'd vote Democrat. His press conference within the hour might make me look naive but my guess is that Christie will stick with his M.O. of pissing off conservatives until he's re-elected. But I think the 2013 vs. 2016 framing for his thinking is a misnomer or faulty construction. I think 2013 is about 2016 (or else more vaguely an eventual presidential run) for Christie. There are murmurs he might try to do the special in October instead of November, but I can't imagine that will actually happen.
EDIT 2: I do look naive on 2 counts. He
did schedule a special for October and the self-serving timing at the cost of tens of millions of taxpayer $ is provoking criticism from right and left. And it also looks like his rhetoric today was laying the groundwork for a Republican pick for the next 4 months.