Actually they did build at least one nuclear-powered NB-36H prototype. AFAIK the nuclear propulsion was only backup for the jets in this one.
Very controversial program even at the time; for one thing, weight savings meant that the reactor was shielded only on the side facing the crew cabin... Meaning that the amount of outwards radiation was disastrous.
Extensive historical and technical data
on this personal page.
BTW, the Soviets, though their atom plane was apparently just mock to scare the SAC dead, did intensive works on a number of nuclear-powered spacecraft launchers...
Search in
here...