My guess is that they will dither. It would be typical of Russia to do such a thing and then deny it, with lots of smoke blown, in an attempt to sow division between NATO nations. And, in any event, I wouldn't expect a single tactical nuclear weapon would mean an inevitable escalation to a MAD-style nuclear exchange - more likely would be that NATO would want to move its troops forward into Ukraine "for security", and perhaps "dare" Russia to repeat the use of nukes.
But the other thing we have to wonder is what state the Russian nuclear arsenal is in. The opportunities, over the decades, for corruption to hollow out such a high-value resource, especially if they believed it would never be used (and they'd never be found out), are legion, and the temptation far too great. Nukes need ongoing maintenance, both in terms of the delivery system, and the bombs themselves. If Russia can't make sure its tanks/trucks/personnel are adequately resourced, why would anyone think that the nuclear weaponry would be treated any better?