The tune at least seems to have been a favorite of frontiersman Davy Crockett's.

"An Account of Col. Crockett’s Tour to the North and Down East" (1835), p. 34:

“Their fiddling [at the theater] was pretty good, considering every fellow played his own piece; and I would have known more about it if they had played a tune, but it was all twee-wee-tadlum-tadlum-tum-tum, tadle-leedle-tadle-leedle-lee. The ‘Twenty-second of February,” or the ‘Cuckoo's Nest,’ would have been a treat.”