100,000 would be more than the Allies initially deployed
As some of you problably know, brazil fought in world war II with the brazilian expedictionary force, 25 thousand brazilians fought in the italian front from 1944 until the end of the war, it was nothing decisive in the war, but they fought bravery and as general Mark Clark said: "I wish my soldiers fought like brazilians"
However, there is something that was proposed when brazil Joined the allies in 1942, the american government asked the Brazilian president Getúlio Vargas to enact a general mobilization and send 100 thousand soldiers to fight in the operation torch in november of 1942, the brazilian government refused of course because we barely had enought rifles to equip our army (heck, 95% of the equipament that the brazilians used in world war II, from rifles to uniforms and even the tanks were borrowed from USA), so here is a scenario: What if the Brazilian army had received more support during the late 30s and early 40s and could help in operation torch and in operation Husky, how could this 100 thousand men change the front?
100,000 would be more than the Allies initially deployed to French North Africa, and there were logistical challenges sustaining the TORCH forces; perhaps that number was the suggested personnel strength for a mobilized Brazilian Army at home?
IIRC, the Brazilian Army's personnel strength at the time the country entered the war in August, 1942, was ~80,000, up from ~60,000 a decade earlier. Historically, I think the CEB (at ~25,000 in the ETO, Army and Air Force) was about one-fifth of the 120,000 or so troops Brazil mobilized during the war?
Given Brazil's internal political situation, presume any expeditionary force in 1942 is going to have to be (at least formally) made up of volunteers; also need a replacement pool, training cadre, troops in transit, etc.
So, maybe one-fifth of that 80,000-strong force, using the same ratio as in 1944, amounts to a field force of 16,000... which is a roughly a reinforced US infantry division in the standard TO&E, so a force equivalent to the 1st Division (1st, 6th, and 11th RCTs) could have been assembled, albeit without the support forces that ended up in Italy historically.
The issue, of course, is that until Brazil assumed full-belligerant status, even with Lend-Lease there is going to be a limited amount of US standard equipment for training in Brazil (as there was, historically) and most of what is immediately available for allied forces in North Africa is going to go to reequip the French. Plus, August to November is really only a couple of months of training time, if that, in Brazil...
My guess is maybe a single RCT as a representative force could be expected to be in North Africa by the end of the Tunisian Campaign in May, 1943; so, all else being equal, the entire 1st Division might have been deployed and available by the time of the invasion of Italy in September. If so, I would expect the division to move to Italy in the autumn of 1943, seeing action around the New Year, 1944, presumably assigned to the 5th Army on the Winter Line at this point:
http://www.history.army.mil/books/wwii/winterline/winter-fm.htm
Historically, the Fifth Army had four corps (from the coast inland, the British X, with the 46th and 56th divisions (and 23rd Armoured Brigade); the US II, with the 3rd and 36th divisions; and the US VI, with the 34th and 45th divisions; and the French Expeditionary Corps, with the 2nd and 3rd divisions; 1st Armored Division was the army-level reserve, along with the 1st SSF, the 504th PIR, and the brigade-sized Italian 1st Group.
Interesting point of departure.
Best,