Ricky Gervais has a comedy bit about this, except he applies it to flies, not spiders. It's pretty funny, regardless.
This confusion is because in Ireland and the UK, a Daddy Long-Legs is a fly (in the US, known as a Crane Fly), whereas in the US it is used to refer to a kind of spider. Well, sort of.
According to an article about the Daddy Long Legs Myth at UC Davis the term Daddy Long Legs refers not in fact to a true spider but to opilionids (see the UC Davis article for more detail; incidentally, there's very common ones in Ireland) but is often used to refer also to spiders. The article also firmly calls the venom/poison rumour out as myth. Snopes agrees, but their source is the UC Davis page, so that doesn't really add much.