Chances are pretty good if you are willing to stay at any of the DVC resorts. January tends to sell out more slowly than some of the other months. SSR is the most likely to have availability, but the others are also possbilities.
That said, unreserved units from the point inventory are often sent to CRO at the 60 day mark. That means you would be competing with the general public for the rooms. MLK weekend could be a problem.
I called today to see if some additional nights were available at SSR in January and at first the Disney cast member said, "No," and I said, "No?? Really??" And then she said, "Sorry, I meant yes. I'm just so used to saying no."