If Putin were to use a nuclear weapon here, wouldn’t that effectively FORCE the US to do the same? Because if we don’t, what’s to stop him from using the next o

If Putin were to use a nuclear weapon here, wouldn’t that effectively FORCE the US to do the same? Because if we don’t, what’s to stop him from using the next one, and the next, and the one after that? Surely Big Bad Vlad is aware of this - he’s not stupid. What i don’t know is whether or not he’s rational enough to care.