In fact this whole thing is being very interesting, because one guy is managing to create multiple diplomatic incidents, I would not be surprised if this end in some sort of war, or a breakup of alliances or trade zones.
I think it all depends on who wins in the end. Too bad, the common people always lose.
[1] I stopped short of saying dumbly.
The entire south america is pissed off for example, and I've seen people here talking about trying to convince europeans to join us in a anti-US war, WWII style (ie: demonize the US and throw the entire world against it).
And it might work, plainly because US policies since WWII mostly pissed everyone off, almost all countries have reasons to want to see US destroyed, and I am pretty sure that with enough incentive, you might end with the entire world attacking the US...
Other possible scenarios are EU civil war, South America vs EU war, or Asian countries starting their own already incoming wars during this chaos, hoping to drag one western country or another to their side.
I strongly disagree about Argentina and Brazil backing America. I'm not sure if you know much everyone hates the US in South America. And for good reasons: Just look at the history of the Americas in the 70s, 80s and even 90s.
And what do you even mean by World War III?
With the info that NATO has been used to spy on the E.U. I definitely see incentive for a separate European military arrangement.