Apple doing it and Spotify doing it are two completely different things, traffic-wise. Assuming that Apple is basing their streaming solution off of Lala's model (not a given, but why else acquire them?), we're talking about giving every iTunes user streaming access to their entire music library, including songs that weren't purchased through iTunes (which would require a serious amount of cloud storage). Spotify reached one million users sometime last year; there are how many millions of iPhones and iPod Touch's out in the world?

Even though the most recent numbers from Spotify indicate something on the order of 10 million users, I agree that Apple still has larger innate audience. However, Spotify uses filesharing to further decrease the load on their own servers, which I don't think Lala used. For some fun details on the Spotify model, see http://www.csc.kth.se/~gkreitz/spotify-p2p10/