Coming from a situation where my wife is the apartment manager where we live...it depends on the owner of the property really.
We require a 30 day written notice, not just a verbal, "hey, i'm leaving on this date."
Why? Because it's part of the lease that you're told about up front and you agree to is upon signing. Just like the noise ordinance, when signing the lease, that's your last warning about having parties and being too noisy.
as mbogosia states, being an owner, for every rent that isn't paid whether late or never, that's $$ out of your pocket. Even if you have to evict someone that's typically more money out of your pocket, especially if you have to get the legal system involved, but you can always sue the person for the $$ but if they didn't have the $$ in the first place for rent, getting the rest might prove rather difficult (ask my sis in-law)
Another reason to try and work something out: Sure you might own a house now, but who knows what the future will hold? What if you're not able to make mortgage and are forced back into renting? Oops! Got a ding on your rental history =/
Also, some places will take you to collections. Why? Well, if one person decides not to pay rent and thinks they can get away with it, what's not to stop the rest of the tenants from doing the same?
My suggestion, talk to your landlord/manager. Unless they're a complete tool they should be willing to negotiate some kind of payment plan for you guys. Especially if you've been renting there for awhile and always have been good renters.
And in your situation, not to be mean, but at our place if someone is looking for a house, we have them fill out a 30 day written notice but with the stipulation that if they happen to need to live there a little longer than intended, they get pro-rated. So an estimated 30 day notice of departure would have been golden. Unfortunately that's in the past for you now =/