The phrase "down to the wire" (modernly, often "under the wire") comes from one of the oldest spectator sports,
horse racing. In olden days, a wire was strung across the track above the
finish line to help the judges tell who crossed first. An observant judge standing by this mark could likely see which horse it was that had been the first to pass directly below the wire. Naturally, horse races are often won by more obvious lengths, but if the two leading horses were so close that the winner could not be determined until one of them passed this crossing wire, the race was heralded as one which had indeed been run "down to the wire," and the horse that won it as the one which came in "under the wire."