Does anyone know when, where and how this originated? What is it referring to?
Horse racing. The wire is the finish wire.
This is a WAG, but I thought the string/ribbon/thin-flexible-material-stretched-across-the-track that marked the end of a race was called the “wire” and that any race that was decided by seeing which contestant broke through it was one that had come “down to the wire.”
Main Entry: down-to-the-wire
Pronunciation: 'daun-t&-[th]&-'wIr
Function: adjective
Date: 1952
: full of suspense; especially : unsettled until the very end
Horse racing was once more popular than football in North America.