LED Museum has spectral power distribution graphs for all sorts of light sources:
Compact Fluorescent
High Power LEDs
The closest I've seen to nautral light are the warmest of the Cree LEDs -- other than a deficiency in deep red, and a slight gap in the "cyan" region (blue/green) they are actually a pretty close match. In the case of the LED I think they have the ability to close that gap and make an extremely natural-looking source.
These graphs can be deceptive though. For one thing, they represent power, and are not weighted for sensitivity -- green will appear brighter from a given light source than what the lines on the graph might indicate. Also, crappy Cool White fluorescent tubes that look absolutely atrocious (60CRI) have a broader distribution of wavelengths than premium fluorescent lamps (that look more "spiky") but the latter actually render color much more accurately and are much less headache-inducing.