I went through this with xp and he did end up leaving. We coped and dd1 and I are WAAAAAY better without him, he would have made as crap a dad as he did a husband.
I then went on to meet dp and have two more children, he did admit to feeling very nervous in the run up to dd2 being born, but he never actually considered leaving.
Your dh may just be having last minute panics about the baby, but he does need to consider that you are actually a HELL of a lot more important than he is at the moment, you have the baby inside you, you're going to go through the birth and you are going to have to cope with the majority of the childcare (I would guess, anyway, given his attitude so far).
He may well fall totally and completely in love with the baby when it arrives, but you have to seriously consider whether you want to be with someone who puts his own feelings and worries SO far ahead of yours, at 40 weeks, he really should be looking after you, no matter how frightened he feels.
If he does leave, you WILL cope, you will be a much better single parent as part of a couple where half of the couple doesn't want to be there.
Good luck.
xx