Holding on by a thread

Hello! New Orleans Mayor said "The people of our city are holding on by a thread". I have never come across this expression. Does it mean the people are in a very difficult situation?

'Hanging on by a thread' would, I think, be more common this (the Eastern) side of the Atlantic. I have always assumed the allusion is to a rope which has frayed until there is only a single thread still intact. A perilous situation.

DFG

Perhaps connected to "The sword of Damocles" ?

"Hanging (not "holding") on by a thread" is pretty common west of the Atlantic. The hanging/holding difference is slight enough that US speakers would have understood the mayor.
~rb in US