(Biech 2009, at p. 152) attributes this quote to Thomas Jefferson. This is the only source I found attributing the quote to somebody other than Edison, so I assume it is in error.
The National Parks Service attributes the quote to Thomas Edison on the page for the Thomas Edison National Historical Park. While this is still not a contemporaneous attribution with details of time, addressee, etc., I treat the Thomas Edison National Historical Park as more reliable than the citations in the question.
Using literally to mean virtually
The use of literally in a colloquial sense to mean virtually has been occuring for centuries, as per the OED (see usage c. colloq.) from as far back as 1769, and notably in 1876 by Mark Twain. Thus, if Thomas Edison used the word "literally" in this sense, that would not be inconsistent with the history of the word.
Biech, Elaine. Ten Steps to Successful Training. ASTD, 2009.
National Parks Service. Thomas Edison National Historical Park. url:http://www.nps.gov/edis/forteachers/index.htm