will we see bitcoin price continue going up or will it crash?
I'm not sure whether the price will hit $20k by january 1st but it's not going to crash either. The price is going to AT LEAST increase to $20k before any major corrections taking place, in my opinion. Not going to be any sooner than that.
Right now we're just on the way to $20k or more, thus you see virtually no change in price in the past few days.
Though if there are negative news coming out before the new year, it could effect the price a little bit. In that case, we'll need some more time to hit $20k, but it'll still happen.