In a horse race, if the horses were together all the way to the finish line, the wire strung above the line, higher than their heads, would help determine which horse's nose crossed first. I found that here: http://www.worldwidewords.org/qa/qa-dow1.htm Any time two or more things or ideas are competing, and it's very close, it can go right down to the wire. You will not know who won until the deadline or time is up.

right down to the wire = it won't be decide until the very last minute