It would really be something if that miniature nuclear reactor NASA tested ended up being viable for cars, realizing one of the dreams from the early nuclear age.
Given that even a small reactor still requires considerable shielding, generates waste that could be used for nuclear proliferation (if ammassed), and emits harmful radiation, I would say chances of a nuclear car for the every man are slim to none.
There's that, but on the other hand, small gasoline vapor explosions are quite harmful and require considerable shielding, and generate waste that is destroying our ecosystem.
The nuclear waste problem seems to be not so severe in the age where everything is tracked every second; and it doesn't need to be solved completely - just raise the cost of (illegal) waste extraction to be considerably higher than getting it from alternative sources, and you're set.