55 million tweets/day * 140 characters/tweet ~= 14.5 GB/day, presuming a 16-bit character encoding.
That's only about 20 TB for four years worth of data, or about $1500 worth of storage, before compression.
That doesn't seem like it would be a significant challenge for the LOC. I'm more interested in understanding why they would want to use that amount of space to archive Twitter, as opposed to anything else.