As an experiment, I'm going to say that this sounds like one of those to me. It feels too much like a modern species, not something from the Renaissance. Now I'm going to go check and report back. :)
Edit: here's what I found. Wikiquote lists it as "unsourced". Google Books shows the phrase as appearing in a few dozen recent inspirational and self-help books (Marry Your Baby Daddy, anyone?), but no scholarly or historical ones (http://books.google.com/books?q=%22greater+danger+for+most+o...). Google web search comes up only with reams of those awful junky quotation sites. It's possible that the wording is a modern translation of an authentic quote, but in general, if 5-10 minutes of Googling doesn't come up with an original source for a famous quote by a famous genius, the odds are against it.
It's still a great line.
thanks for all the work; i came across the quote a couple of years ago (i believe google was not even "big" then) and never bothered to check back (for this post i just googled and found a couple of attributes, just for reassurance--obviously i should have been more careful)
nevertheless, i think it's a great quote, too. (i find myself citing it from time to time, about twice a year or so...)
ps: i know a couple of italians, probably they will be able to clarify on etymological issues...
The greater danger for most of us is not that our aim is too high and we miss it, but that it is too low and we reach it. --michelangelo