When something is left ‘down to the wire’, it has been left to the very last minute to be completed or decided. Maybe there’s a deadline and everyone had to work right up to it, with no time to spare. The clock is ticking, your Boss is waiting for the order to be fulfilled or the monthly sales figures to come in, and everyone is still working hard. They are going to take this 'right down to the wire', doing the best they can until the very end.
Maybe the pressure is on; maybe someone is racing and they are ‘neck and neck’ all the way through the race. This time it is going to go ‘down to the wire’, because the outcome will not be clear until the very last second of the race, when someone passes the finish line. It might be a draw, but there is no way to anticipate it.
So, if something did not happen until the last possible moment, you might hear someone say ‘it came right down to the wire’. If it is difficult to guess what might happen, someone might say ‘this looks like it will go down to the wire’.