If either side had the means to increase the intensity of the fighting and were willing to accept the consequences of doing so, they would have done it.

In my opinion, the question makes sense more as an inquiry into deterrence options.

If discussing deterrence, it would probably be best to set aside talk about nuclear weapons. Here's why I think that is.

Already in the early 1950's, a doctrine of massive retaliation (ie nuclear) was articulated by Dulles. He was not referring merely to an attack on US or NATO, that was already understood. The issue of the day was conflict along the edges, at that time in Asia. The massive retaliation doctrine was a more powerful alternative to the doctrine of mere containment, where the French in Vietnam and US in Korea had already run up against limitations of power projection. Dulles' bluff was, arguably, called as the French were defeated in Vietnam. The key conclusion then drawn about the Dulles paradigm, was that

If the Communists should challenge our sincerity, and they would have good reasons for daring to do so, we would either have to put up or shut up

The quote coming from Kaufmann 1954, as quoted in Farooqui per link below. Thereafter policymakers shifted away from such a hyperbolic escalatory conception of deterrence, toward one in which there was a graduated spectrum of options. The above is taken from a somewhat critical history by Farooqui 2019, a sometime grad student of Adam Tooze's.

As it applies to this Question, the part about having to "either put up or shut up" applies equally to other first-class players, I.e. USSR becoming Russia and also China. The threat can be made, and it has been (eg Cuba missile crisis) - but ultimately it is too obvious that nobody wants to end the world.

As far as nuclear weapons go, the lack of credibility of such threats applies even more today, as the bluff has been repeatedly called so many times. It's just not a useful line of conversation, as there are many lesser options which are also quite destructive.

Despite that, I hope it is clear that all involved are far more vulnerable than to conventional weapons they care to admit, including even the US.

In the case of the US, Russia is not even the primary rival. It is China. From a geostrategic point of view, US has to stay in this contest just to maintain "credibility" with respect to China - not to a friendly audience such as found here, but rather to the governments of Asia and Africa. This is also a vulnerability that can be exploited by Russia, as the US faces crises in other theaters (e.g. the Red Sea, or bases in Iraq). It is a line of attack would be much more strategically economical for Russia, than deliberately starting WWIII.

If either side had the means to increase the intensity of the fighting and were willing to accept the consequences of doing so, they would have done it.

In my opinion, the question makes sense more as an inquiry into deterrence options.

If discussing deterrence, it would probably be best to set aside talk about nuclear weapons. Here's why I think that is.

Already in the early 1950's, a doctrine of massive retaliation (ie nuclear) was articulated by Dulles. He was not referring merely to an attack on US or NATO, that was already understood. The issue of the day was conflict along the edges, at that time in Asia. The massive retaliation doctrine was a more powerful alternative to the doctrine of mere containment, where the French in Vietnam and US in Korea had already run up against limitations of power projection. Dulles' bluff was, arguably, called as the French were defeated in Vietnam. The key conclusion then drawn about the Dulles paradigm, was that

If the Communists should challenge our sincerity, and they would have good reasons for daring to do so, we would either have to put up or shut up

The quote coming from Kaufmann 1954, as quoted in Farooqui per link below. Thereafter policymakers shifted away from such a hyperbolic escalatory conception of deterrence, toward one in which there was a graduated spectrum of options. The above is taken from a somewhat critical history by Farooqui 2019, a sometime grad student of Adam Tooze's.

As it applies to this Question, the part about having to "either put up or shut up" applies equally to other first-class players, I.e. USSR becoming Russia and also China. The threat can be made, and it has been (eg Cuba missile crisis) - but ultimately it is too obvious that nobody wants to end the world.

As far as nuclear weapons go, the lack of credibility of such threats applies even more today, as red lines were crossed repeatedly over the years. It's just not a useful line of conversation, as there are many lesser options which are also quite destructive.

Despite that, I hope it is clear that all involved are far more vulnerable to conventional weapons than they care to admit, including even the US.

In the case of the US, Russia is not even the primary rival. It is China. From a geostrategic point of view, US has to stay in this contest just to maintain "credibility" with respect to China - not to a friendly audience such as found here, but rather to the governments of Asia and Africa. This is also a vulnerability that can be exploited by Russia, as the US faces crises in other theaters (e.g. the Red Sea, or bases in Iraq). It is a line of attack would be much more strategically economical for Russia, than deliberately starting WWIII.