This HAS TO spell the end for Putin. I think your analysis is spot on. Putin is a bully and an egomaniac that completely underestimated the Ukraine and the West. Now, he's facing embarrassment, and his ego will never let him back down, so he throws the nuke threat, as a hail Mary to instill terror and get the West to back off.
If we back off now, it'll be a huge mistake. It will embolden him for future stuff. The truth is his latest threat is that of a terrified and desperate man who made the wrong move and is trying to save face. It's like the schoolyard bully who steps his torture up a notch when you resist his attempts to take your lunch money. We have him on, or near the ropes from what I can see....but that's just my opinion