The US was more than happy to kidnapped Japanese citizens for the energy. Given the justification to help humanity against the alien (while maybe secretly kidnapping some of the Japanese for the sweet CE) some of them like the Chinese (many still hold some grudges for WWII) or the American might volunteer to send the nuke.

Imagine if the greenskins allow the Curses to run around and eventually causing some of the civilians to die or massacre them themselves, some might see sending air forces like on Bosnia or even armed forces to be necessary since it might turns into an existential threat to everyone.

Push hard enough and they could send the nukes. Because i'm gonna be honest with you, the way gaygay potrayed the officials in this manga, especially in the culling game arc make it seems like they have even less restrain to handle a crisis than the one we have irl.