Yes, if content storage was involved, it certainly could become a drive hog. There are two ways this could go.
The first is obviously a limiting one where no content beyond links is stored. This alleviates most of the space requirements but brings in a vulnerability of stale links. Doable, but not preferable.
Second, is the possibility of cloud storage. If a well organized system of RAID type pointers could be devised, the data could simply float around on the drives of people running the site. When it was called for, certain mirror systems would gather the locations and a call for it would be done in standard RAID fashion. This means that if one part isn't available at the time, the same data can be generated by 2 or more other systems. Obviously, the numbers would have to be tweaked as viewing habits and site popularity changed but it's certainly doable. Fortunately, that's a ways off with 2+ Terrabyte drives around $100.
I really enjoy the possibility of the data actually residing "no-where" so the government has no power over it. ;)