You realize that if relations really broke down to that level, then most likely NATO would simply exclude the USA, it wouldn't be all of the other NATO members leaving it, right? Also, if it gets to the level that the EU / Europe would feel they no longer want a military alliance with the USA, then it's likely that they wouldn't want to counter just Russian and Chinese influence, but US influence as well - there's nothing inherently better about US influence than the other two (Chinese influence so far has been the least bad outside of China itself, out of the three, by far - though I have no delusion that this will continue as China's power grows).