It's day 2 and we've been trying to always have 1 of us awake at all times watching the baby so that we're never both sleeping at the same time. Does a newborn need to be watched 24/7 or am I just stressing out over nothing? The baby is sleeping in the same room as us, but I'm worried about sleeping through the crying or any problems where she doesn't cry that I need to watch out for.
Yes, it's okay for both parents to sleep at the same time, for several reasons.
The human mind is finely tuned to the sound of crying babies, you'll be surprised at what you can hear subconsciously while you sleep. Our pediatrician wisely commented that newborns have only one desire - to grow older - so you can be sure they'll tell you if something is bothering them enough.
Another reason to sleep together is that parents need to take care of each other too. If you always put the baby first, then you'll burn out. You can only care for the baby when you're
adequately reasonably sort of rested and balanced.
The only situation where "keeping watch" might be sensible is if you're very worried about SIDS. The problem is that "sudden" really means "science has no idea what causes this and there seem to be no symptoms", so nobody can say if this child is more/less at risk. For parents that are worried specifically about SIDS there are products like Angel Care but mostly you've just got to accept that you can't prevent some things. Also, as KennyPeanuts points out, SIDS is very rare and often misunderstood to include suffocation from objects (teddys, pillows, blankets) so be sure to have a safe crib those first few months.
If both of you sleep in close proximity to the baby, so that you can hear her cry or even mumble when she does, you'll be fine.
Your "Something Odd Detection System" will be on 11 even when you're sleeping, in the first months.
You'll be surprised how alert you can be in an instant. It is almost as if you are sleeping, but you are not. We have a new born (our 3rd) and you get used to what sounds are ordinary and which aren't. She's 4 weeks old and actually did a proper cry, for the first time, a few nights ago and we both jumped out of bed.
Just take time to get to know their noises, to know their snuffles, their sqeaks, everything they do, and you'll become very aware, very quickly about who they are. All of mine were different. This one actually sounds a bit like a baby animal in the room.
During the day, we move her around in a moses basket and leave her by the dishwasher, washing machine (they seem to love noise near them, that's fairly consistent) and we'll both catch a bit of shut eye. Trust me, you'll hear her. As Roy said, your senses are around about 11 at the moment, especially if it is your first.
But most of all, your child will benefit the most from having alert parents around and for that, you both need a good amount of sleep and I'd advise you get it when you can. Lie in the same room as him/her and you'll love listening to him/her and will doze off as content as you'll ever have been. Enjoy it!
When we had our first, we would check on her many times throughout the night. Everyone told us that we were being silly but we'd still check every time she made a noise (or worse, didn't). After a while, we bought an Anglecare baby monitor that included a motion detector - if the child stops breathing, then an alarm sounds. It is probably overkill, but it allowed us to get a decent night's sleep, a rare commodity with a young baby.
My wife has the primary responsibility of getting up in the middle of the night and dealing with kids. We have three children, we both sleep at the same time and she still get's plenty of sleep.
Make sure your kids eat a good dinner and go to bed at the same time every night. This will help you get your sleep.
To answer your question, it is perfectly fine for both parents to be sleeping at the same time. My wife is very alert. When my wife was in the hospital having another baby, I was responsible for the kids, I normally sleep very hard and it's impossible to wake me, but when it was my turn I was very alert knowing that I needed to monitor them at night.
It's completely safe for both parents to sleep at the same time.