M.J.
He will go on a 'strike' to get you to relent. Be consistent. Keep offering the sippy cup with milk. Also offer yogurt, cheese, cottage cheese, etc.
My daughter did the same thing. We were consistent and eventually she gave in and began drinking milk out of the cup more. It took a month! We tried all sorts of cups too. To this day, she doesn't drink much milk, but prefers yogurt and cheese over milk. We also have her take multivitamin liquid daily.
It took about a month to get her to begin drinking more milk! But it varies - most I heard was it took several weeks or just 2 weeks. Each child is different. But in the end, it won't affect them developmentally or physically, and they will never 'starve' themselves.
Don't fret; lots of kids do this. It's not the end of the world -- he will eventually drink it and in the meantime try other methods of calcium intake. Milk is not 'all that,' there are other equally healthy ways to get calcium in the foods mentioned above.
Cold turkey is hard, for mom as well as the child, but in due time he will come around. We all have been there. :o) Congrads on stopping the bottle!