I had never considered burning the candle at both ends to mean anything other than setting light to both ends of a candle.
A quick web search brings up http://www.phrases.org.uk/meanings/burning-the-candle-at-both-ends.html which reckons the meaning "both ends of the day" is one added fairly recently.

I also found an interesting video - Buring a candle at both ends.

Quack!
GtD.