Roughly: the state-space of the universe isn't large enough to contain a distinct physical realisation of every book in Borges' library, though it is about large enough to contain every possible tweet (I think.)

Yep, that's it exactly.

The calculation goes like this:

There are about 10^80 elementary particles in the known universe.

No physical process can happen faster than the Planck frequency (the frequency of light at which a single photon would have enough energy to form a black hole), about 10^43 Hz.

The universe is about 10^16 seconds old.

Multiply all those numbers together and you get 10^140 = 2^465.

Even if you allow 10^100 seconds (a conservative estimate of the time until the heat death of the universe) you still only get about 2^700 possible enumerable states.

Of course, if you want all the enumerates states to exist simultaneously then you can only encode one state per particle, and the number drops to 10^80 = 2^265, about 53 5-bit characters, not even a third of a tweet.