This is a very interesting thought. The Argentinians could have their very own "stab in the back" myth come out of this one...(1)
Would they have until the summer? I know that there quite a bit of pressure to negotiate in the UN. If there's a whole winter without the task force coming in, does that pressure mount? (2)
1) Didn't Chile support Argentina in the UN? They may have been playing a double game.
2) The failure of Haig's shuttle diplomacy meant the diplomatic option was dead. Argentina started off with a naked act of military aggression against a nuclear power. The aggressor being a military dictatorship and the victim a democracy. It would have been a very bad precedent to allow a military dictatorship to get away with that. Basically, once Argentinian troops got their boots on the ground, it was going to be either Thatcher or Galtieri who had to go. The contrast between the two leaders was obvious.
But they were far from crap when fighting the British, and actually put up a good fight on land. (3) I'm wondering how it would have gone down if troops closer to the quality of British soldiers had been deployed instead of badly outmatched young, poorly trained conscripts.
Also, to all of you thinking that Chile would invade, why would they? (4) They had no reason to start a war. I doubt they would do anything unless Argentina attacked.
3) No, they didn't. The Argentine Air Force fought like lions, but not it's army. The exceptions were in cases of individual heroism, and the (3rd?, 5th?) Argentine Marine Battalion, who faced 5 Brigade in the fighting in the hills before the fall of Port Stanley. But even there, they lost at the hands of what was considered the "poorest troops"

the British had in the Falklands.
4) Indeed correct. The Chilean military MIGHT have wanted to, but even in Pinochet's dictatorship he had to consider, at some level, the public opinion polls in Santiago. Which were heavily pro-Argentinian on this single issue. Doing a little dirty work to tweak Buenos Aires' nose was one thing. Launching an all out war with a country you were going to have to live with after the fighting was all over was another.
How many wars had Argentina fought between 1900 and 1982? (throwing nuns out of helicopters doesn't really count) (5)
How many had Britain? (6)
5) Yeah. The Apartheid South African Army got the shit kicked out of it (to their utter shock) at the hands of the Cuban Army in Angola. Because the Cubans had a real (by Soviet standards) first class army and the Apartheid South Africans were mostly trained and equipped for constabulary work, suppression of revolts, and defeating invasions by poorly trained, poorly equipped, and poorly led African armies crossing the dry arid open country on South Africa's borders.
6) Duh. The British Army is the best trained most combat capable army in the world for its size.

The average British infantryman is better than his US Army counterpart all the way up until you get to the level of special forces and above. And the troops the British sent to the Falklands were anything but average.

The Argentines could have sent the absolute best they had and it wouldn't have changed anything.
The Argentines sent far too many troops (elite, conscript, and otherwise) to the Falklands than could be supported logistically. So not only should they have sent better troops, they should have sent far less. Say, about a third. Which would have brought the British much closer to a reasonable troop ratio for invasion anyway, thereby negating the qualitative improvement of the Argentine garrison. Also, the inevitable defeat of the Argentine Navy and Air Force would mean that even the better Argentinian troops would have been facing the same morale problems as the draftees did. Only simply just on a strategic level only ("...they abandoned us...!"), not tactical. No frozen feet, no ration shortage, and so on. But the sense of hopelessness will still have an effect. Especially as the British close on Port Stanley.
The British still would not have needed to wait until summer. Their chosen invasion landing sites were indefensible. The Argentine commander would have needed to put nearly his entire force there to have a chance at victory, thereby uncovering all the other possible landing sites (except Port Stanley, where the beaches were too limited in size and had too much firepower in place). That would have enabled the British to basically outflank the Argentines and swoop right into Port Stanley from the sites in the south or north (unlikely in the north, as the waters there were rough and too open, plus there is a land isthmus making for a bottleneck).