Until 1964 it looked like GM would make their own Cobra rival, indeed perhaps they would even make 2 rivals!
The first path was the Corvette Grand Sport, and ultra light version of the Corvette Stingray currently being produced to the tune of about 22,00 units per year. The prototype GS was first track tested in December 1962 but word came from on high in January 1963 that all racing efforts were to be stopped and the FIA homologation application was withdrawn. However the final 3 of the 5 GS' were developed and raced by private entrants with limited support through 1963 and in October were sent back to Chev for modification including the all-alloy, quad-Weber 377 engine. With these mods the 3 GS' went to Nassau and kicked arse, again drawing the attention of the GM brass determined to shut down racing. While being prepped for an endurance race at Daytona in Feb 1964 the brass came down hard and the cars were quickly disposed of so they couldn't be destroyed.
The second path is basically the opposite of the Corvette Grand Sport. Racing identity Bill Thomas was given covert support by General Motors Performance Product Group head and connected private investors to develop the Cheetah as a concept vehicle. The support basically came in the form of major components which were installed in a custom fabricated concept car. The idea was that 100 Cheetahs would be built for homologation, but the rules changed for 1964 requiring 1000 vehicles so the design wasn't properly refined but went into limited production anyway with attendant problems. Even this effort was ruined by a fire in Thomas' shop in Sept 1965.
So is there any combination of factors that sees one or both of these cars built in homologation numbers?