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Some notes on the Jumo 004 turbojet engine that powered the Me 262:

Development on the Jumo 004 began in 1939 under the direction of Anselm Franz, whose experience with turbocompressors built on the pioneering turbojet work of Hans von Ohain. The model 004A flew for the first time on 1942, but was not suitable for production because of its high weight, and large content of high-temperature alloys, which were in short supply in Germany. The 004B production model was easier to manufacture, weighed less, and utilized air cooling of the combustor, turbine blades, and exhaust nozzle. First production engines were delivered in mid-1943, and volume production began in 1944, with close to 6,000 Jumo 004 engines built by the end of World War II.

The Jumo 004 was the world's first mass-produced turbojet engine, and first to incorporate afterburning and a variable area exhaust nozzle. Although its major application was the Me 262 fighter, it also powered the Ar 234 twin-engine light bomber and reconnaisance aircraft.

http://airandspace.si.edu/collections/artifact.cfm?object=nasm_A19670124000

There have been debates about earlier production of the Me 262, and how Hitler's decision to delay production was a mistake. Such discussions usually don't take into account the technical aspects of mass producing the engine. From the above, it appears that the Germans didn't have a version of the Jumo 004 that was capable of mass production with the scarce resources at hand until 1944 anyway.

So it didn't really matter.