'But me no buts' is an expression that, rather unusually, we seem to be able to securely trace to its origin. According to Wiktionary it appeared first in the 1709 play The Busie Body, by Susanna Centlivre.
But is a very interesting word, like many of the short unobtrusive words that help glue the language together. In Old English it was butan, 'unless, without', compounded from by + utana, meaning something like 'at out', and it only acquired the modern sense of an objection from the 14 century.
The second element is from ut, 'out', which is ultimately from a Proto-Indo-European root *uidh-, 'up, out' that also (apart from out) also gives us words such as utter, utmost, carouse (from German gar aus, 'well out'), and astonishingly, hubris.
In Modern English this usually means overweening pride or foolhardy insolence, but Ancient Greek ὕβρις signified something more: blasphemy or behaviour that was lacking in proper reverence, outside what was acceptable. In the Iliad Achilles desecrates Hector's dead body and this hubristic act leads to Achilles own fate.
Of course but me know buts is a formula that can be used with more or less any word in place of but, but a rather witty example dates from the 1960s.
The US postal service needed to standardise the abbreviations used for the 50 states to all be two letters. Up until then there had been considerable variety and many people felt attached to the traditional abbreviations, so the changes met with a fair bit of resistance. Utah in particular was happy with 'Utah' and put up a stiff fight against becoming 'Ut'.
If you can't guess their campaign slogan look again at the title of this post!