I presume you mean 7.62mm ammunition, or 30-06?
276 Pederson was developed for the Pederson semiautomatic rifle, but there were several variants of it and one was considered for the earlier versions of the M1 Garand. It was, as you say, an intermediate: it had a muzzle energy of 1858 ft-lbs, as opposed to a ME of 2500 for the standard M2 load of 30-06. That would still have been fine, putting it into the class of something like 7x57 Mauser, and the shorter, slightly-less powerful cartridge was meant to cycle more easily in the semiautomatic Garand. There would have also been a savings in weight of ammunition transported, and also perhaps a few ounces could have been shed from the Garand as well. But as .276 Pederson was in development in 1932 the Army Chief of Staff, General Douglas MacArthur, reviewed it and disapproved of any caliber reduction. And that was that.
Frank Barnes: Cartridges of the World