A significant chunk of people in Russia already believe that they are in World War 3 against NATO, given the level of support Ukraine has received. I don't know what's going to happen now though. As many Western analysts say, Russia has "no viable exit strategy", but neither do the Ukrainians, nor the Americans. I am guessing that the American leadership may end up doing what they usually do and pour a ton of resources into this conflict, turn it into a gruesome quagmire, then years later just abandon the satellite government to its inevitable demise as they did with Afghanistan, Vietnam etc. That seems a bit weird to me, as the stakes are quite a bit higher this time given that they are dealing with Russia, but maybe they are negligent enough to do something like that.