To be wrapped around the axel is to be in a difficult situation from which it’s hard to extract oneself. It seems that anything with an axel, from a horse-drawn wagon to a wheelbarrow, has been considered a possible source.
Phrase Finder had some hypotheses but no citation. But here’s a citation I found in wikipedia:
As The New York Times noted in its obituary of the dancer on 15 September 1927, ‘The automobile was going at full speed when the scarf of strong silk began winding around the wheel and with terrific force dragged Miss Duncan, around whom it was securely wrapped, bodily over the side of the car, precipitating her with violence against the cobblestone street. She was dragged for several yards before the chauffeur halted, attracted by her cries in the street. Medical aid was summoned, but it was stated that she had been strangled and killed instantly.’
Ug! Certainly dramatic enough to stick in the public mind and perhaps become this phrase.