I don't see why this particularly matters. You could likely store the entire twitter archive on a couple of memory sticks, so it doesn't seem to warrant some big library to "house" it.
I think this is big for a few reasons. One, if its in the LoC then it is (probably) available to the public. Previously it wasn't. That's pretty big.
Also with the LoC having a public archive of it, we can keep better track of politicians who post things online- always a good thing since occasionally they shift their positions or outright lie.
As a data analyst, I'm really excited.
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.