At most places I've been (including my own grad school experience), the grad students live by the motto "work hard, play hard." So, you bust your butt, work killer hours in the lab, juggle research, teaching, and in my case a residence life position as well, but then you also have to make time for yourself, and when you get that day you can take off, or a long weekend when you miraculously can get out of the lab, you make the most of it.
It is harder to find time for a social life, but you shouldn't deprive yourself of it. Everyone needs an outlet outside the lab to keep from burning out. The hardest part of developing a relationship with someone is getting them to understand why you can't just leave the lab at 5 pm and head out on a date with them, or why it is that everytime you say you'll be done around 7, you don't really leave until 8 or 9.
Just like all things related to dating, it's going to depend on you and where your priorities are. If you find someone you really want to be with and she's that important to you, you'll find time to spend with her (you might find you're more efficient at running several things simultaneously in the lab when you have the incentive to leave early for a date). And if it isn't all that important to you, you'll probably spend more time in the lab. I personally found that grad school was perfect for nurturing a long-distance relationship...you don't have time to see each other anyway, and I could find time to take a day off once a month when my boyfriend could visit me or I could visit him, and it didn't really matter if I called him from home or from the lab when we wanted to talk late at night (email wasn't an addiction yet then, people still spoke on the phone).