I really doubt Claire will die because of the whole thing about her having to raise the baby herself. That's why she's on the island, after all, because the psychic knew if she got on the plane she'd have to raise it herself. If he foresaw the plane crash, he probably could have foreseen her dying in childbirth. Plus, they've barely shown her at all in recent episodes - if she was going to die, they'd probably lead up to it by giving us at least a few last scenes with her.
I'm not sure why everyone seems to think the death has to be a shock. There are certainly going to be shocks before the season is over, and I'm sure we're going to have a kick-ass, jaw-dropping cliffhanger, but I doubt it'll be related to a death. The death is likely what will open the door for all the other shockers; not the actual shocker itself. After all, a death is an end - the things that will truly shock us have to present possibilities of new beginnings and give us things to theorize on and go crazy about all summer.