Wiktionary disputes this theory as to the origin of the phrase, on the grounds that the first written reference to the cat o' nine tails was in 1695 – 30 years later than the first authentication of the phrase "not enough room ... " (1665).
It seems to me, however, to be perfectly possible that both idioms had been in use orally for some time before they were written down, which would make it nigh–on impossible to say which came first. I am extremely sceptical regarding the idea favoured by Wiktionary – that the "not enough room ... " saying is a reference to the actual swinging of a feline quadriped.
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