Actually, the White Council has significant physical assets. Jim has spoken several times about the various locations owned by the White Council apart from the castle under Edinburgh, not to mention their enormous financial holdings (likely several hedge funds or similar). Even if the US got upset, the White Council would probably return to Europe where their influence is strongest. I doubt they would be overly upset if the US kicked them out.
What I think will be interesting is seeing how the other nations react. Not to mention, the USA has enough enemies circling it. An enormous, terrifying internal threat might be more than it can handle. Don't think for a second that the enemies of the US wouldn't take advantage of such a situation. More on this in another thread.
As for the Warlock execution thing...I don't think they would mind. I think they would prefer if their own authorities did it, and I suspect the White Council wouldn't object. Ideally they would work together. It would be trickier in states that don't have the death penalty. Often when countries invade other countries some locals side with the invaders. Sometimes for a chance at a better life, or because they feel oppressed by their own government, sometimes they are forced into it. It's an ugly world sometimes too. But I suspect that the US would probably (at least initially) want those with the know-how to help them catch and probably kill other supernaturals. Of course, what happens when it's only the "good" wizards left? Us mortals tend to fear what we don't understand and cannot control, and hate what we fear. So likely, they end up killing them too. Assuming they win the war against the bad guys.