There are two problems that I can see with overnight success, the first being: it doesn't really exist. The second is, it can be proven to exist.
This sucks for writers because, no matter how much we say we know it won't be easy and that we're willing to put the work in (and in fact, no matter how truthful we're being when we say it), all of us hope - and I would say that deep down, a lot of us believe - that somewhere along the way, somewhere in the midst of the sweat and tears and restless nights, something will just go whoosh and we'll wake up one morning to a book deal on our front step and a talk show host begging for a prime time interview.
Of course, it doesn't really work like that. It can't, unless you know someone, or at the very least, know someone who knows someone, and even then there are no guarantees. But we keep hoping, because after all, overnight success can be proven. This is because, to the public, every success seems like it happened overnight. Take someone who is ludicrously rich and famous. Say, Lady Gaga. She seemed, to the majority of people, to spring out of nowhere. First, there was nothing, then there was Just Dance and Poker Face and suddenly everyone knew who she was - but she'd been performing for years before that. It's pretty much the same way with all celebrities (including celebrity authors), because most of us don't know anything about them until they're already famous - so to us, they go from 0-famous in, at the very most, two seconds. Proof that overnight successes not only happen, they happen every day.
Part of this proof, I think, can also be attributed to the fact that we as writers (and the more I think about this, the more I think I should say we as Westerners) really, really want to believe that by tomorrow, we could have everything we've ever wanted - so even if famous authors come out and say, I did X for years and years and I worked really hard to get an agent and then I did Y, we tend to only catch the end of it. The bit that goes, And then Z was published and the next thing I knew, the phone was ringing off the hook.
I blame it all on Cinderella. Here's a girl whose life sucked, who worked hard, who learned all sorts of useful skills like sewing and communicating with animals, but who was ultimately content to stay where she was - and what we're supposed to remember about her isn't that she worked hard or faced injustice bravely; it's that one day, her problems magically disappeared and she got everything she'd ever dreamed of. Stupid fairy tales, filling our heads with fluff.
... of course, they were right about true love and the prince...
...so we can hope.