As an experienced nanny it actually kind of puts me off when someone offers me the job right away (like at the end of the interview). It feels like a rushed decision that the parents didn't take much time to think through, and it puts me on the spot. I would much rather them sit on it for a few days. I've also found that a lot of families will say they are still interviewing other people when they actually aren't, but they say that to be polite when really they just want time to think.
If it's been over a week or two I would assume that I didn't get a job, and I would continue my search. Usually by that time it means they've chosen someone else, and they will only offer you the job if you were their second choice and the first turns them down.