Well, the only part of my story that was overnight could have been a disaster.
I sent out my first handful of queries a couple days before Thanksgiving in 2005. Really just testing the waters (and getting pressured by my writing group!).
The next morning, I had a response from an agent who sounded very excited, wanted to see my first 100 pages.
However, things quickly began to feel sticky once I'd sent the pages and we had a phone conversation. Agent was very critical, made a sort-of offer if I agreed to major re-writing under the agent's tutelage.
Only then did I start doing more research, found AW, realized agent had not much of a track record and an "iffy" reputation.
Politely, with mutual good wishes, we ended our discussion. I kept on querying.
Nine months later, I got an offer from a solid NY agent. A year later, we had a publisher. The book came out in January 2009.
My overnight success story
(This was my first book, however. And I'm in my 50's. So that part of the story should offer encouragement.)