China was not nuked, not because the US feared the political backlash, but because nukes just wouldn't have been militarily effective as a battlefield weapon. If the US nuked Chinese cities and killed civilians, then it would've put itself at risk of Soviet reprisals in Europe or even against the US mainland.
Korean War
Korean War - Wikipedia, the free encyclopedia
In October 1951, the US effected Operation Hudson Harbor to establish nuclear weapon-use capability. USAF B-29 bombers practiced individual bombing runs (using dummy nuclear or conventional bombs) from Okinawa to North Korea, coordinated from Yokota Air Base, in east-central Japan. Hudson Harbor tested “actual functioning of all activities which would be involved in an atomic strike, including weapons -assembly and -testing, leading, ground control of bomb aiming”. The bombing run data indicated that atomic bombs would be tactically ineffective against massed infantry, because the “timely identification of large masses of enemy troops was extremely rare.”