I know I have no real reason to worry, but I just figured out that:
a) Legally, to give 30 days notice, I need to send my current landlord written notice immediately, today (and hope that the mail isn't delayed)
yet
b) the new place's property management company won't want to sign a lease until at least Monday, partly because they want to contact my current landlord as a reference.
So the worst case I suppose is that if it falls through, I will either:
a) apologize, beg my landlord's forgiveness (ick)
or
b) scramble to find another place
Small chance, I know. Yet I am twitching.