What is the origin of the phrase "One Day At A Time" and what does it mean?

It probably came to A.A. from the Oxford Group and it seems similar to the meaning of "practicing these principles in all our affairs." There's no reason to believe it as anything to do with "not drinking" one day at a time.

The phrase is not to be found in the main text of The Big Book, but it does appear in personal stories published in The Big Book and in other AA literature, including As Bill Sees It and Twelve Concepts for World Service.

The phrase does appear at the very end of The Oxford Group pamphlet called The Four Absolutes. That booklet ends with this paragraph:

Remember our four questions, "Is it true or false?", "Is it right or wrong?", "How will this affect the other fellow?", and "Is it ugly or beautiful?". Answering these queries every day with absolute integrity, and following the dictates of those answers one day at a time, will surely lead us well on our journey toward absorbing and applying the Absolutes.

Since A.A. grew out of The Oxford Group and the pamphlet pre-dates the beginning of A.A., this Oxford Group concept and pamphlet appear likely to be the source of the phrase.

Thanks to the Anonymous Press website FAQ page - http://anonpress.org/faq/files/

Here's another place mentioning "one day at a time"; the Serenity Prayer attributed to Reinhold Neiburh:

Serenity Prayer
God grant me the serenity to
Accept the things I cannot change;
Courage to change the thngs I can;
And the Wisdom to know the difference.

Living one day at a time;
Accepting hardships as the pathway to peace;
Taking as He did, this World as it is;
Not as I would have it.

Trusting that He will make all things right if I surrender to His will;
That I may be reasonably happy in this life
And Supremely happy with Him,
Forever in the next.