But the problem is the economic and political situation in Argentina. The Argentine economy was in bad enough shape without the Junta trying to build up arms for a serious conflict and any kind of drawn out war with the British would have undermined the Junta. They only moved because they had convinced themselves(with considerable help from the Thatcher government) that the British were prepared to abandon the Falklands.
The treasonous activities of the Whitehall Mandarin's and their decades long crusade to be rid of the Falklands inspite of any public opinion or Government policy to contrary beggars belief.
Other than Thatchers governments efforts in reducing public spending resulting in the navy being slimmed down (including the decommissioning of HMS Endurance) - they had very little to do with the Junta's decision making process - or certainly no more than previous governments who had repeatedly failed to make a decision on replacing the Eagle and Ark Royal (unless you consider no decision as a decision?)
In response to the OP - unless the Junta can hide its efforts (unlikely) then HMG is going to build up a garrison as fast as they can and send approximately 'Some' Hunter Killer Nuclear subs to the area, strongly worded letter to the times and pressure from the various 'friends' of Britain etc
On the subject of Nuclear weapons - it takes more than the prime minister waking up crazy one morning to order the release of Nuclear weapons! Its not going to happen.
Some one suggested that Nuclear Depth charges were on board some of the ships that started out from Gibraltar. This is true but they were handed over mid journey to an RFA ship which returned them to the UK.
They never entered the war zone as far as I know.
Basically eve if they do provide the island with more troops etc so long as 3rd Commando brigade gets ashore with enough supplies - then the Argies lose.