I am stressed. My wife is expecting a baby. I am happy but at the same time I feel littlle stresse by the responsibilities.
Yeah, I know how you feel. Not exactly the same situation, though. I was going through with an adoption, but same amount of responsibilities nonetheless. 
Did it go away after the adoption happened?
Well, yes and no. There's ups and downs, but you get used to the responsibilities. Just expect more stress from your wife than anything else.  