It's always facinating to learn a little more about how these contracts were made.
The is what Clark Campbell has to say on the matter in his "The '03 Era" (1994):
"In order to meet the demand for even more rifles (largely for the foriegn requisitions of Lend-Lease), a contract had been proposed, in January 1942, with the High Standard Manufacturing Corporation, of New Haven Conn., for 100,000 rifle, M11903A1.
High Standard, however, was already heavily overburdened with war orders and agreed to accept the contract only on the condition that they be allowed to subcontract to the L.C. Smith & Corona Typewriter Company the manufacture of all components except the barrels.
It was decided that, on this basis, the prime contractor really should be the L.C. Smith & Corona Co.
On 24 Feb. 1942, therefore, Smith Corona was given a letter order for 100,000 M1903 (Modified) rifles, as were being produced by the Remington Arms Company. Deliveries were scheduled to begin in late September.
With the approval of the M1903A3 rifle on 21 May 1942, tooling for the nonstamped metal parts (using machinery acquired by the purchase iof the nearby Fox Arms Company, a subsidiary of Savage Arms Corp.), was of course, compleated for that model.....
The pilot lot of 20 rifles of M1903A3 type was finished on 24 Oct. 1942, with volume production beginning with 5,540 rifles completed in Dec. 1942. [Ed. Note: 3 months behind initial optimistic estimate] These rifles, besides using sub-contracted barrels (including a few 6-groove ones supplied early in the game from commercial tooling by Savage Arms Corp.), were fitted with stocks made on subcontract."
So they really did put up a big arms plant on bits and pieces gathered catch as catch can. 480,000 or so rifles is nothing to sneeze at.
I suppose it was (mainly?) Remington who supplied the stamped parts, as orsogato notes, barrels came from High Standard (mostly?), while their own tooling came from Fox Arms (mostly?). It would be interesting to know who made the stocks.