Like a lot of others have said here, it depends on where you define your threshold for having "learned" a language. To get reasonably productive in a language to the point where you can (eventually) build most things shouldn't take more than week if you have a few under your belt.
Then there is the long process learning the right idioms, keeping up with the latest changes in newer languages, familiarizing yourself with the universe of libraries, etc, etc - I think all of these things are required to really claim fluency in a language. So I would answer "a long, long ass time."
Agreed, a week for basic literacy and years for mastery. Based on my own experience I'd say it takes two years of using a language every day and following news groups to be able to write it idiomatically. Every year after that helps you get stuff done (knowledge of tool chains, packages, and the dustiest corners of the language) but the returns are diminishing.
Code from those early days of basic literacy are the thoughest to look back on. "Hey, why does this perl code look like it is trying to be C++?"
Then there is the long process learning the right idioms, keeping up with the latest changes in newer languages, familiarizing yourself with the universe of libraries, etc, etc - I think all of these things are required to really claim fluency in a language. So I would answer "a long, long ass time."