I read a story a few days ago where one of the people involved was hinting the story might continue into season 4, and I am really hoping it won't. It's barely held my interest for once season, I'd really rather not see them drag it out for two.
With three episodes left in S3, i'm sure the producers will milk every scene of potential death, fighting and tragedy possible right up to the last frame of the season finale.
Many seem to think the governor plot will carry over into season 4, but that's just dragging out a plot that cannot believably continue--even for an audience already suspending disbelief about the central plot of zombies.
I could see the Woodbury plot carrying over to Season 4, but not the Governor plot.
I liked the little bit of dialogue when the Governor mentioned that he was at work "taking shit from a boss half my age and with an IQ to match," and I think Rick has him pretty well sussed out.
As for Andrea, she is a frustrating character but from her conversation with Hershal I think she knows that she belongs with Rick's group. I think she still hopes that she can convince some of the Woodbury people to not go ahead with the attack, she seems to see herself as a peacekeeper.
Regarding character deaths, I don't actually want any of the prison lot to die. Beth is the obvious one to assume, but I'd like her to stick around. They seemed to be setting up a sort of love-triangle between her, Rick and Carl. But who knows what the producers are thinking. I'd like to see Merle stick around for a while longer as well just because it's fun to have an unstable element in the show.