This would likely make a great natural language data set for compression algorithms.
True, but doesn't Twitter already provide an API for access to a fraction of the firehose? Surely that would be enough data. If Twitter doesn't have a good API, Reddit allows full access to all comments through their API (although Reddit has orders of magnitude less data).
Twitter's API is too limited for historical data. (you'll hit the rate limits quickly for any meaningful volume). Reddit's rate limits, however, let you process a million comments every day.