Funny thing is that I nuked USSR and my popularity actually risen.
EDIT: Canada and Mexico are asshats.
Yeah, attacking enemies tends to make your popularity rise. I invaded Libya after the CIA told me they were behind the destruction of a chemical plant killing 100 and my popularity went from 53% towards the upper 70%'s
They also had Soviet troops aiding in their defense, it would make sense Libya would attack me since they were allied with the Soviets.