Can I have more than 12 objectives in my deck with this affiliation card?

We may have to wait for rules insert with the first pack, but I'm pretty sure the deck requirements are meant to be read as an exclusive description (ie the deck must contain exactly the mix described on only that), not as a minimum (ie the deck must contain exactly that number of Smuggler and Rebel/Neutral, and then any number of Jedi). So unless new information comes out between now and then, I'd assume the answer is "no."

No need to wait, FFG actually responded to a rules question about it:

Q:
Are the deck building requirements in th spoiled affiliation cards for the Alliances cycle meant to be exclusive? For example, does Desperate Allies mean that the objective deck must contain exactly 10 cards (5 Smuggler and 5 Jedi/Neutral) or at least 10 cards (5 Smuggler, 5 Jedi/Neutral, any number of Rebel)?

A:
“Exactly” means: no more, no less. So, your objective deck will have exactly 10 objectives in it, no more, no less. You cannot add any additional objectives beyond the amount listed on the card (so, 5 Smugler and 5 Jedi/Neutral, for example).

--
Erik Dahlman
LCG Developer