If NATO, through private channels, said to the Russians "start to leave Ukraine in 36 hours or we will enter Ukraine through Poland and force you out. We will not enter Russia," do you think Putin would use nuclear weapons?
They've already called that bluff, it's no use attempting to bluff again. The current bet is that NATO will not get involved militarily because doing so is armageddon. They knew there would be sanctions and they knew there would be material aid so whatever they have planned will play out on a short enough timeline that the sanctions won't starve it and with some number of predicted losses. I don't think they've fully played their hand yet, it seems like they're setting something up.
I think odds are good he would nuclear strike kyiv. But not the west.
They should say it through public channels then.
Saying it privately gives the Russians a chance to negotiate something with Ukraine and/or act like this operation was a short incursion and save face.