Cats, our apartment, and our first baby

Hello...

We're having our first baby due in May, and we have 2 cats. We also
live in a 2 bedroom apartment for now (hopefully next year we'll get
our first house).

We vaccuum and try to dust often, we have hardwood floors and mop and
all that. So we're not dirty people, but we're not super clean where
we vaccuum EVERY day or mop EVERY day, once/twice a week kind of
thing.. i think that's fairly typical...

The wife is mroe emotional than I am as a person, and she's very
attached to the cats.

Will the baby have any problems with asthma or anything like that
growing up with 2 cats?

My wife is perfectly healthy and "normal" having grown up in a house
with 8 cats, and i grew up in a house without ANY pets.

So am i being paranoid and over-protective in wanting to think about
getting "rid" of the cats?

I just want the baby to have a close to healthy and perfect
environment to be raised in and i dont want her to have asthma or
anything.

Thanks!

.