同意黎老师的分析！下面从另一角度作个补充：句中的 until the last minute 也可视为固定搭配，意思是“直到最后一刻”“直到最后一分钟”，它除与动词 wait 连用外，还可跟其他动词连用。如：
He will probably wait until the last minute. 他也许会等到最后一刻。
Don’t leave it all until the last minute. 不要把什么都拖到最后一分钟。
We were scurrying about until the last minute before the party. 聚会开始前我们一直不停地忙忙碌碌。
Everything was fine until the last minute, when she suddenly got cold feet.  一切都很顺利，但到最后她突然胆怯了。
I had fallen into my old bad habit of leaving everything until the last minute. 我又恢复了过去什么事都要拖到最后一分钟才干的坏习惯。
How on earth did you know I was coming today when I didn’t know myself until the last minute? 你是怎么知道我今天会来的？我自己都是最后一刻才知道的。