That 12 US divisions across the Atlantic is only achieved in Aug 1943.
I think the reason why Aber is completely correct deserves consideration.
After the 1942 landings in France were cancelled, U.S. Army Chief of Staff GEN George C Marshall sent two divisions, the 40th and 43rd U.S. Infantry Divisions to the Southwest Pacific, and ordered the 2nd U.S. Cavalry Division broken up to form the 9th U.S. Armored Division. After the Casablanca Conference delayed the assault until 1944, Marshall released the 1st U.S. Cavalry and 6th, 7th, 31st, 33rd and 38th U.S. Infantry Divisions to the Pacific. Thus, four of 15 precious pre-Pearl Harbor Regular Army divisions were among nine total U.S. Army divisions lost to employment at all in the European Theater, although six of them underwent specialized training for combat in Europe during 1942. Moreover, to avoid overburdening transatlantic maritime supply lines, Marshall kept all combat-ready divisions in the United States except the 82nd and 101st U.S. Airborne and the 36th and 45th U.S. Infantry Divisions until actually required in Great Britain for Operation Overlord.
Ina ddition, the British Army was stronger in 1942. A dozen divisions, including the 1, 8, 9, 10, 42 (East Lancashire) Armoured, and 38 (Welsh), 44 (Home Counties), 45 (Wessex), 47 (2 London), 48 (South Midland), 59 (Staffordshire) and 61 (South Midland) Divisions were combat ready in 1942, but broken up or gutted to provide replacements for combat losses in Italy (1943-4), India (1943) or early on after the Normandy landings (mid-1944). Additionally, a plan to form 2 Guards Armoured Division from 6 Guards Armoured and 24 Guards Brigades was abandoned in late 1942 because the prospect for its employment in France was not pressing.
So as many as 21 additional Allied combat divisions could be available if the Iberian Peninsula were an active combat theater in 1942. The training level, quality of equipment, tactical doctrine, leadership, etc. of the American troops may be less, but the lessons learned are on a much broader scale.
As for US Corps HQ, two were used in Operation Torch - II Corps under MG Lloyd Fredenhall in Algeria and MG George Patton's I Armored Corps under the designation Western Task Force in Morocco. In addition, V Corps under MG William Key arrived in Great Britain in January 1942. Active in the United States in January 1942 were I, III, IV, VI, VII, VIII and IX US Corps.
All of this is modified, or dependent on when Spain joins the Axis, and when and whether Portugal does as well.