While I don't know of any specifics, I wouldn't doubt it. A group of state congressional delegations working in concert could get the job done though.
Again, where did you get the idea that Arnold is planning to sue he feds over protecting the borders? All he has said is that he's going to go to them to get money. He hasn't said just how he plans to do that. You're guessing that he means to initiate a lawsuit of some sort; I'm not. I have no idea how he plans to do it. Unfortunately, from all indications, neither does he, at least not yet.