There are several mutations of this around.
carpe diem is Latin for "seize the day", from the Latin phrase used by Horace. basically, this is a descriptive term for literature that urges readers to live for the moment. In modern times we have adopted the phrase quoted by you. I've heard several versions. "don't put off today, what you can do tomorrow" and "don't put off tomorrow what you can do today!"
But I do believe it has its origins in the 16th and 17th Century.
The theme, which was widely used in 16th- and 17th-century love poetry, is best exemplified by a familiar stanza from Robert Herrick's "To the Virgins, to Make Much of Time" :
Gather ye rosebuds while ye may,
Old time is still a-flying;
And this same flower that smiles today
Tomorrow will be dying.
Shakespeare's version of the theme takes the following form in Twelfth Night :
What is love? 'Tis not hereafter;
Present mirth has present laughter;
What's to come is still unsure.
In delay there lies no plenty,
Then come and kiss me sweet and twenty;
Youth's a stuff will not endure.
I don't want to get to the end of my life and find that I lived just the length of it. I want to have lived the width of it as well.
- Diane Ackerman, quoted in "Newsweek"
