It's big, but not beyond what already exists. There are already databases in the petabytes region. 1 petabyte can hold 10 billion 100kB images.
The point was not that it can't be done; it certainly can and Google and MS already have such gargantuan databases. But Flickr alone has over 5 billion images. My point was that it's
very expensive to setup and maintain. I'm talking Fortune 50 company resources here. Datacenter with "just" 1 petabyte costs in the
millions in
storage hardware alone - add to that setup, software development, maintenance, cooling, security, electricity, etc.
Not sure how TinEye works, but there's certainly a lot of raw CPU power at their datacenters to do the pattern matching on all those images since they don't do bit-by-bit matching - again adding to the cost. We're talking a big warehouse full of cutting edge hardware and software ran by an army of specialized engineers.
If there's no money in running such a database to turn a profit, nobody will do it. Public money is probably not an option, either, given the state of the world economy and cost.