While living in Patagonia (Puerto Madryn, Neoquen, and Bariloche), I couldn't help but see the similarities of the Patagonia and the American-South-West.
Alternate Timeline
1984: The US and the USSR engaged in an all out thermal-nuclear war. (The Day After).
The US, Europe and large parts of Asia are reduced to radioactive-wastelands.
Surviving Americans head to the West-Coast where there's less radiation and board ships and sail as far as they can away from the North; they sail all the way to South America, which was untouched by the nuclear exchange.
It's hard to say how many Americans fled south, but enough to have an impact in the societies of Chile and Argentina.
Problems:
1. Though Argentina can feed 100 million people if need be, the area in which the Americans landed is a desert similar to Nevada. There's little food and Catholic Missions have to feed these American-refugees.
2. The Americans refuse to assimilate to Argentine society; they remain protestant and refuse to learn Rio-Platenese Spanish. They consider themselves to be Americans and not Argentinians.
3. The Americans brought their guns with them.
4. It wasn't the city folk that survived, it was mostly the rural-folk who knew who to live off the land; the majority of them are conservative and were Republicans.
5. Mass-graves: a lot of American refugees experienced contact with large doses of radiation. Many died at sea and still more died when they got here.
6. Increase crime / tension. Whenever you have a large group of disparate people who have lost it all and have little to lose, you're going to run into problems. The Argentinians will consider Americans barbarians due to their behaviors. Conflict is inevitable.
Benefits
1. A few Americans bring their engineering and medical skills and improve the over-all standard of living in a decade or so.
2. The Americans, mostly being rural and have no interest of going to Argentinian cities, fit in just fine. The majority Argentinians dislike the country and would rather live in their cities. Works out nicely.
Summery: in the end, I see the Americans settling on the coast and in the Mountains and in a few decades, becoming fully Argentinian while keeping some of their heritage like American-Football and in the names of the new cities they found; New Washington (spelled Nuevo Wallingon (pronounced, "Wahshenhon")).
The threat of a conflict is likely and even with some of some of the technology the Americans can bring with them like Stinger missiles, they can retreat to the Andes and wage an effective guerrilla war against the Argentinian military.
Also, there's no British fleet now that's going to sail South to protect Falklands so they'd better get used to the hearing, "Shama mate, claro?"