First of all, congrats!
I have a three and half month old (first child) - I'd classify our income as probably the same as yours based on what your post states - we have a decent mortgage, only 1 car payment. Good insurance. Some fun money.
That said, i just wrote the checks for the birth. Without getting too exact, we're right about $2,500 out for it. We also had about $8k in savings prior to her taking maternity leave. When all was said and done, by the time she went back to work we were down to the last couple thousand $ in the savings. But we also spent about $2k of the 8k on house projects that couldn't wait until winter and while we 'tried' to be frugal, we didn't really live as cheaply as we could have.
The Missus breastfed/pumped for the first two months or so and we now mix 2:1 with formula so we were going through a can of it (Nutramigen - The expensive shit) a week or so. This saved us a ton of money in the beginning.
Now the wife is back at work Tuesday and Wednesday for 11 hour shifts and her mom is watching Charlie until i get home around 5. Then it's just me and him until around 9. And on Saturday, her other long shift, i watch him all day.
We're pretty lucky her shifts are awesome and we have her family close by and are able to use them for child care, around here (Minneapolis, MN) daycare is about $1300/month for 5-days a week. Which is absolutely crazy.
Now on to the advice:
If everything's going well, have your wife breastfeed as long as possible. It saves you tons of money and is nutritionally far better during the first few months than formula could ever be. Read up on this stuff.
Disconnect your DTV service , keep your internet, and keep an eye on your cell bills.
If you have a flat panel TV (who doesn't?) buy or build up a computer (Can be done for ~$400) to hook up to it and stream everything you could ever want off the internet with services like Netflix
Streaming or Hulu all in glorious HD. Sure you may not be seeing the show's Live and may need to wait a few days to see them, but when you're sitting on the couch feeding the baby for 30 minutes, you won't care. Sure it's a chunk of cash up front, but it will pay for itself in 4-5 months of not having DTV.
Do as much home and vehicle work as you can before the baby comes!
I really thought i'd have more time to work on the house (finish those projects i started...) and the truck, and my motorcycles, and prep the house for winter etc... but you just don't. And the odd thing is, you'll find yourself wanting to spend time with the kid instead of working on things that need to be done and/or were fun.
Don't buy any new baby clothes unless they are on clearance. The first 3 months, they'll only wear the outfits a couple of times before they don't fit. Also, hit up neighbors and friends for their old baby cloths, we got boxes full for free!
I think i could go on and on... but this is getting lengthy.
TL;DR - Cut your TV, have $7-10k minimum in savings before baby arrives, be ready for the hospital bill to arrive and you'll be just fine.