When the wine ran short during that wedding party at Cana in Galilee, Jesus was there to make up the shortfall in superabundance.
I suggest below that the wine can be said to symbolize our own human efforts in contrast to what Jesus is prepared to do for us. (That's probably more of an accomodation than a genuine spiritual sense of the passage.)
But it isn't just our individual efforts that come up short. Entire movements and whole societies reach the limits of human nature, crest, and collapse.
Even the faithful among the Chosen People, those who obeyed the Law given them by the Lord, were doomed to fail.
So then the law is holy, and the commandment is holy and righteous and good. Did the good, then, become death for me? Of course not! Sin, in order that it might be shown to be sin, worked death in me through the good, so that sin might become sinful beyond measure through the commandment.
The Law convicts those who do not obey it -- which is to say, everyone. But:
...the law of the spirit of life in Christ Jesus has freed you from the law of sin and death. For what the law, weakened by the flesh, was powerless to do, this God has done: by sending his own Son in the likeness of sinful flesh and for the sake of sin, he condemned sin in the flesh, so that the righteous decree of the law might be fulfilled in us, who live not according to the flesh but according to the spirit.
A positive way of expressing this (although we shouldn't gloss over the negative fact of sin) is to say that even obedience to the Law is not enough for us, because what we desire -- stripped of the distortions of our fallen nature -- is union with God. We can't join ourselves to God, but God can join Himself to us.
Sooner or later, the wine of the Law runs short -- and this even if we observe the custom of serving inferior wines as time goes by. When this happened in Israel, there was the Son of God to give them a new, and better, wine. When this happens in our own lives, there is the Son of God to refill our cups with the best of wines.