thats a good point. I bet for an acute existential threat the major powers would nominally ally themselves against it, while still playing politics. So NATO, Russia, China, India, and whomever else would throw their hat in.
We see that if the threat has a long tail though (climate change) that nobody gives a shit.
Neon Genesis Evangelion had this as a sub plot. They could only have 2 or 3 EVA's 'battle ready' at any time in one country depending on when in the series you are. I want to say it was pointless politics but... Yeah, right concerns, wrong application.
There are so many stories from WW2 about how Americans didn't unite.
Here's one of my favorites Patriots complained about air crews painting naked ladies on their planes. They were fine with kids getting drafted and sent overseas, but God Forbid they thought about S*X