Preserved by oral tradition, a proverb like this one is a saying that expresses a general truth or practical observation about life.
In life, radical changes cannot happen overnight and it takes time to accomplish great things. It took centuries for the ancient city of Rome to grow from a small city state to a vast empire, caput mundi - the capital of the civilized world.
Like the building of Rome, in times of stress, just stay the course and be patient.
When Vonnegut repeated this proverb in his novel Cat's Cradle, he wasn't the first to use it and he won't be the last. In 1546, John Heywood used it. The saying has also been traced back to 1545, translated as follows from the medieval French:
Rome ne fut pas faite toute en un jour.
Rome was not made in one day...)
This cliché is so famous that singer Sam Cook wrote a song about it: "I'm gonna make your love as strong as mine/But I know Rome wasn't built in a day."
So did Amy Grant. "It takes a little time sometimes, to get your feet back on the ground...it may not be over by morning, but Rome wasn't built in a day...give it, give it time."
Have patience; it may take a couple of days.