Spore is written with very very little code, all executed by algorithms. I'm 100% sure the DS can handle it.
Actually it's more code because it has to generate not only the game logic but the content as well.
And more stuff to run = more CPU usage. Never mind that the scenes in Spore should involve large numbers of objects (buildings, creatures, etc), none of which were built by someone who had the technical limitations of the system in mind (because they are built by the end user)