A "Fine" Romance

I heard a song called "a fine romance." But I don't quite understand what "fine" means here.

I look it up in the dictionary and "fine" usually means "something good".

But the lyrics are about a girl whining about her romance.

Is the song writer trying to be sarcastic or does "fine" actually mean something that is "acceptable"?

Here's part of the lyrics:

A fine romance, with no kisses
A fine romance, my friend this is
We should be like a couple of hot tomatoes
But you're as cold as yesterday's mashed potatoes
A fine romance, you won't nestle
A fine romance, you won't wrestle
I might as well play bridge
With my old maid aunt
I haven't got a chance
This is a fine romance