I suggested if the Hungarian rebels were better organized in 1956 and able to push away the Soviet troops from Budapest, the Soviets might nuke the city.
(I admit this was inspired by how, in the Draka novels, rebels took over the city of Barcelona and the Draka nuked them.)
Someone with more knowledge of the USSR said the Soviets weren't nearly as "stern" as the Draka and it was more likely they'd simply keep attacking the Hungarians conventionally.
However, I did read that the Soviets lied to the soldiers they sent to Hungary, telling them they were going to Egypt until they actually got there, and they used tanks in Budapest to limit opportunities for fraternization with the rebels. There were Soviet troops executed later for refusing to fire on protesters.
Maybe the Hungarian rebels do better and the Soviet leadership starts fearing a mutiny. However, conventional aerial bombardment would get the job done without outraging everyone the way nukes would.