You don't have to consolidate, just move people: move the occupants of room n to room 2n and now you have infinitely many empty rooms (all the odd-numbered ones).
edit: I see that the folks in 2n would now be in 4n, and so on down the chain. You'd always have some guests that are in the process of being evicted (i.e. between rooms); then again, that's negligible because we're not talking about real life (™). Clever!
I believe David Hilbert was the first to describe this paradox. Source: http://en.m.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Gr...