No, we don't have any theory of the origins of such constants. In fact, constants like c are hard to even discuss, because they have different values in different units (cm/s, m/s, mph, etc.)
When physicists work on theories to explain the values of constants, they pick constants which have no units, i.e. are just plain numbers. An example would be the ratio of the masses of the muon and the electron. Another would be the fine structure constant, 2πe2
/hc, where e is the electronic charge and h is Planck's constant. For the most part there are no established theories accounting for the values of these dimensionless constants either.
One queasy possibility is that physical reality contains domains with all sorts of different values for these constants, but that nobody is asking about them except in the peculiar domains where they are just right to allow life to form. If one accepts that sort of 'anthropic' reasoning, then the explanation of many of these values will be in terms of how they allow complex chemistry to exist, while other values wouldn't.
(published on 03/09/11)