I dismissed it out of hand although the Germans had not. In World War II, they developed the cannon-armed Me 163 interceptor that was rocket powered and had very high performance. One of the first aviation books that I remember reading as a preteen was Rocket Fighter by Mano Ziegler, a WW II Luftwaffe pilot who flew it. Although legend has it that the Komet was more dangerous for its pilot than the B-17 crews that he was attacking, it was reportedly easy to fly and phenomenally fast for the time. The main problem was its fuel, C-Stoff (57% methanol/ 30% hydrazine/ 13% water), and oxidizer, T-Stoff (80% concentrated hydrogen peroxide / 20% oxoyquinoline. The combination was hypergolic, meaning it ignited just from being mixed, without the need for an ignition source. The Germans developed a process for safely fueling the Komet but a crash on takeoff or landing (particularly from the rough-and-ready fields available) was likely to result in an explosion or fire.
It turns out that the rocket-propelled interceptor proposal was a paper dated 8 June 1950 that was written by a U.S Navy officer, Commander Robert C. Truax, who was also literally a rocket scientist. It was a summary description and analysis promoting the development of a destroyer-based, rocket-powered interceptor. In this case, furfural alcohol was the fuel and nitric acid was the oxidizer. A small engine was provided for services and cruise; a much larger one provided the thrust and control for vertical takeoff and acceleration.
In Truax's mission scenario, the interceptor would be launched vertically from the fantail of a picket ship, in this case a Gearing-class destroyer that would carry five of the aircraft.
After a flight profile measured in minutes, it would descend by parachute to the sea, from which it would be recovered to be prepared for its next mission.
The range depended on the profile flown, ranging from zero ballistic (70 nm) to full ballistic (150 nm). Top speed was about Mach 4.
(Note that the full ballistic profile meant a recovery about 80 nautical miles from the launch point for a straight-out mission.)
An AN/APS-25 radar was to be used to locate and navigate toward the incoming bombers. 1,500 lbs of the 13,000 lbs gross weight was allocated to the weapons, which were yet to be defined. Aerial mines detonated by proximity fuses were one possibility.
In his paper, Truax noted that significant experience had been gained since the war with liquid-fuel rockets, including over 200 flights of the Bell X-1 with a rocket as its sole power plant. The Douglas D-558-2 was about to fly with a rocket engine. The smaller rocket engine in his design was one in development under contract to the Navy.
Although far-fetched, Truax's proposition received formal consideration at the Navy’s Bureau of Aeronautics and garnered at least one letter of support. However, even if the Korean War hadn’t become a distraction shortly thereafter, it seems very unlikely that the Navy would have taken any action on his rocket-powered interceptor after BuAer's review.
Truax retired from the Navy in 1959 as a Captain and went on to a career at Aerojet, after which he founded his own company, Truax Engineering. Among other things, he designed the Skycycle X-2 for Evel Knievel’s Grand Canyon jump. For more on Truax, see http://en.wikipedia.org/wiki/Robert_Truax .