Millions of colors in the visible spectrum can be generated by mixing red, green and blue - the RGB color system. Is there a basic set of smells that, when mixed, can yield all, or nearly all detectable smells ?
There are about 100 (Purves, 2001) to 400 (Zozulya et al., 2001) functional olfactory receptors in man. While the total tally of olfactory receptor genes exceeds 1000, more than half of them are inactive pseudogenes. The combined activity of the expressed functional receptors accounts for the number of distinct odors that can be discriminated by the human olfactory system, which is estimated to be about 10,000 (Purves, 2001).

Different receptors are sensitive to subsets of chemicals that define a “tuning curve.” Depending on the particular olfactory receptor molecules they contain, some olfactory receptor neurons exhibit marked selectivity to particular chemical stimuli, whereas others are activated by a number of different odorant molecules. In addition, olfactory receptor neurons can exhibit different thresholds for a particular odorant. How these olfactory responses encode a specific odorant is a complex issue that is unlikely to be explained at the level of the primary neurons (Purves, 2001). 

So in a way, the answer to your question is yes, as there are approximately 100 to 400 olfactory receptors. Just like the photoreceptors in the visual system, each sensory neuron in the olfactory epithelium in the nose expresses only a single receptor gene (Kimball). In the visual system for color vision there are just three (red, green and blue cones - RGB) types of sensory neurons, so it's a bit more complicated in olfaction.

References
- Purves et al, Neuroscience, 2nd ed. Sunderland (MA): Sinauer Associates; 2001
- Zozulya et al., Genome Biol (2001); 2(6): research0018.1–0018.12

Sources
- Kimball's Biology Pages
