Considering it was designed for an intermediate cartridge, I'd say off the top of my head that the action was never meant for a high powered cartridge. That's risking disaster just due to the higher energy of the larger calibers.
Furthermore, you're looking at some serious modification to get the action long enough to accept the longer cartridges. The mag well isn't long enough, the bolt stroke may not be long enough to gain return momentum for stripping a new longer cartridge, etc.
Now, it could be possible to take the basic SKS action design and modify it (i.e. beef it up, make it longer) for a larger caliber. But as for just rebarreling an SKS for something like .308 or .30/06, I'm going to have to go with the answer of "that's a bad idea".