Well, we DID develop the aircraft power plants for bombers in the early 50s. I guess if you're going to drop nukes, who cares about the crash of a nuclear-powered aircraft.
Wikipiedia... The US Aircraft Reactor Experiment (ARE) was a 2.5 MW thermal nuclear reactor experiment designed to attain a high power density for use as an engine in a nuclear-powered bomber. It used the molten fluoride salt NaF-ZrF4-UF4 (53-41-6 mol%) as fuel, was moderated by beryllium oxide (BeO), used liquid sodium as a secondary coolant and had a peak temperature of 860 °C. It operated for a 1000-hour cycle in 1954. It was the first molten salt reactor. Work on this project in the US stopped after ICBMs made it obsolete. The designs for its engines can currently be viewed at the EBR-I memorial building at the Idaho National Laboratory.
In 1955, this program produced the successful X-39 engine, two modified General Electric J47s with heat supplied by the Heat Transfer Reactor Experiment-1 (HTRE-1). The first full power test of the HTRE-1 system on nuclear power only took place in January 1956. A total of 5,004 megawatt-hours of operation was completed during the test program. The HTRE-1 was replaced by the HTRE-2 and eventually the HTRE-3 unit powering the two J47s. The HTRE-3 used "a flight-type shield system" and would probably have gone on to power the X-6 had that program been pursued.
President Kennedy changed the course. He wrote "15 years and about $1 billion have been devoted to the attempted development of a nuclear-powered aircraft; but the possibility of achieving a militarily useful aircraft in the foreseeable future is still very remote" in his statement officially ending the Aircraft Nuclear Propulsion program on March 26, 1961. 