Apple has stated that you have 30 days to purchase the warranty with a new phone release. This might be different after
the initial crunch, but Sprint forgot to put AppleCare+ on 2 of mine, I was able to add over the phone with no problem.
Another alternative which I am looking at is Square Trade, which offers a 3 year warranty for $124, covering 4 occurrences.
They also do not need to see the phone, just sales receipts, or in this case, they know the earliest you could have purchased
is release date.
Off the initial subject, but on it about Apple Care