In reply to CrustyRedXpress :
Per the link you posted, the quote given from Putin is “This will mean that NATO countries – the United States and European countries – are at war with Russia. And if this is the case, then, bearing in mind the change in the essence of the conflict, we will make appropriate decisions in response to the threats that will be posed to us.”
There are a number of points here. First, it's a translation. My Russian is almost non-existent, but I'd like to see what words he actually used, and then determine if there is any nuance in that. Beyond that, look at the carefully-chosen language. He never says Russia is at war, but that NATO is - it's a passive construction, designed to reinforce the narrative of Russia as victim to a domestic audience. Nor does he make any sort of direct statement about a response, just that the "appropriate decisions" will be taken in response to specific threats. It's pretty clear that he is trying to maintain a lot of ambiguity, likely because 1) his options are limited, 2) he doesn't want to take undue risks, and 3) he can't afford to be seen domestically as backing down.
So what happens if US/UK approval for ATACMS and Storm Shadow to be used inside Russia? It all depends on how they are used. Right now, the whole debate is centered on two Russian capabilities: recently-delivered Iranian ballistic missiles, and glide bombs. I have no doubt that if approval is given (it was not granted after the most recent talks), it will be for use against the former, and possibly the latter, but that's it. I'm sure there's concern about the optics - US-marked missile parts littering the Russian landscape and showing up on Russian television - and also about reinforcing Putin's narrative. As for Putin's response, it will be measured and asymmetric.
On the last point, to clarify something I mentioned earlier, if Russia were to attempt a repeat of Cuba in 1962 and place nuclear weapons outside the country, note that when this was done it Cuba, the Soviets retained full control over all nuclear weapons and release authority; any such movement now would surely involve the same restrictions. The real question is whether there is any country willing to host such a force in the current security environment; Venezuela might, if Putin guarantees that Maduro stays in power, as might one or two African nations, though access could be a problem. I consider it a low probability event, but not out of the question.