The whiskey on your breath
Could make a small boy dizzy;
But I hung on like death:
Such waltzing was not easy.
We romped until the pans
Slid from the kitchen shelf;

 ‘Like death’ is a vague  simile . On the surface, we understand that death is something inevitable— something that won’t let go of us. Yet, there are also spooky connotations associated with the idea of ‘death.’ 
 
 Perhaps the speaker is remembering his father’s death. Or maybe the experience frightened him, making him fear for his life. (Remember, these are the memories from childhood, so you’ll have to forgive  hyperbole .)
My Papas Waltz