What you'd be looking for here isn't voice recognition. Rather, you're looking for particular tones and their relationship to one another. It's the "shape" of the sequence of tones that is of importance in identifying the song, since that shape is the same regardless of the musical key you're using (or even if you're singing "between the keys"). Rather than trying to make sense of it, you're just extracting frequency and duration from the sung notes. Then the raw notes are pretty easy to express in compact yet human-readable formats like ABC or Lilypond. Indexing it by the "shape" of the tune would be akin to indexing names using the Soundex algorithm. I'd be really surprised if that's not what's already being done.
The rate of growth is far, far less than what Google normally handles.
To address George's problem, I'd recommend something like a Flash version of iABC (http://abc.sourceforge.net/iabc/) in which you can tweak the tune until it's acceptable to your ear, then submit the search. The problem with a virtual keyboard is that hunting and pecking leaves you with the problem of expressing the notes' durations and musical rests. Not everybody knows the piano keyboard, and even those that do can't be expected to play it with a mouse.
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