When a babies nose is stuffed up they will have a harder time breathing and may be more fussy but the baby won't completely stop breathing from a stuffy nose.
The baby can still breathe through it's mouth so the baby won't suffocate from the stuffy nose although it's still a good idea to try to get the babies nosed cleared up.
You can use a humidifier in the babies room to add moisture to the air which can help clear the babies congestion and stuffy nose.
Use suction device for the babies nose as well to help clear the babies nose out.
Walmart also sells a Nose vacuum that is safe for babies, children and even adults to help suction the snot and mucus out of the babies nose.
Also you could place a pillow under the baby bed mattress to help elevate the babies head a bit which can help the baby breathe better.
The babies stuffy nose should clear up within a week or so and the baby will be okay.