We were worried too about this as we have two big fluffy (and very pushy) kitties but it never ended up being a problem. A couple of times I noticed our cats trying to step from bed to Moses basket (when DD1 was a newborn) but then thought better of it after bub stirred or the basket started rocking or both!! Once she was big enough to move to the cot in her own room they definitely weren't interested as by then she was much more active and they didn't like it when she moved in her sleep.
Now she's 11 months and crawling and pulling up on furniture, our biggest fears are that she's going to get scratched by one of them as she's always trying to "pat" them (screaming DATDAT! at the same time) but they generally keep their distance if they know what's good for them! She loves the cats, she gets more excited to see them than us!