[Vash02]

Britains military defence of the Falklands has been significantly increased since the 1982. there's a proper airfield now with four Typhoon fighter bombers patrolling.
There's also the new Type-45 frigate has been sent to guard the islands. The Type-45 is the most advanced AA ship in the world. That single frigate could take out South America's entire airforce.
Then there's always the unknown number of nuclear submarines that could be patrolling the waters.

So yeah, Falklands are pretty much secure. Argentina isnt going to take it by force.

On the political side of it, I'm thinking the president is just banging the drum and trying to get some support up for her government. She isnt serious about taking the islands back by diplomatic means. The UK has made it clear they wont allow Argentina to have them without the Islanders consent and she has done nothing but bully them so far.