etymology - What is the origin of "tall tale"?

A tall tale is a folkloric story that is generally wildly exaggerated and told for the amusement of the listeners. Tall tale tellers usually claim some sort of personal involvement in the story. I was curious about the origin of the phrase itself, and in the course of poking around, I found that tall in this phrase means exaggerated, so "tall tale" means an "exaggerated story."

What I can't seem to find is where this term originated. It seems to be sometime in the middle to late 1800s in the US, but who coined this term? Was it a famous author? Did someone publish a book of tall tales around that time?

(More specifically, the argument revolves around whether or not Mark Twain was responsible, although if it's not him, then who?)

EDIT:
According to Etymology Online, tall "meaning 'exaggerated' (as in tall tale) is Amer.Eng. colloquial attested by 1846." (Now I will look to find where it is attested in 1846.)

Another Edit:
An additional bit of interest is that a tall tale is considered folklore, and this word (folk-lore) was very famously coined by William Thoms in 1846.