It sounds like he is the type of person who gets overwhelmed and then just won't do anything. It looks like laziness, but I bet deep down inside he wants you to be proud of him, and he wants to be proud of himself.
If I were you, I'd do it in stages and help him ALL THE WAY. Like others have said, kicking him out won't do any good. You'll need to get his dad on board too. I know what you mean about the Divorced Parent Guilt. My husband suffers from it too. When his daughter doesn't do what should be expected, he goes all Divorced Parent Guilt on her and lets it slide.
I would give him some timelines and options. Why did he drop out of school? Was it too hard? Was he not interested? Did he just not have the follow-through? He needs someone to talk to him and LISTEN to him, not just make him wrong for dropping out and not having a job. What does he want out of life? He may not know, or have no idea how to get it.
I would give him a month or so, and then he moves out of his room and onto the couch. That should be an incentive to get his own place, but he's not homeless. You could start charging him a small amount of rent when he gets a job (to prepare him for what it's like when he moves out). Save the rent but don't tell him, and then give it back to him to use as a deposit on an apartment.
Go apartment shopping with him so he can get an idea of how much it will cost and what different price levels look like. It might also get him excited and motivated.
You're going to need to "hold his hand" but I think with love, patience and a little bit of a kick, he'll be getting ready to live the kind of life he wants!