If the Falklands were a US territory, the Argentines would have never attacked at all because they would have feared US reprisal on many fronts, not just militarily. US diplomatic and economic sanctions would have been crippling alone.
I doubt the US would have attacked the Argentine mainland, but the fear probably was that the US *could* strike the Argentine mainland anytime, anywhere. I think there's some small chance that the US could have hit a coastal base used to support the invasion, if only as a demonstration of power and as a means of getting Argentine to hide their assets before the US hunted them down.
The US would have done what it usually does, establish air supremacy, deny any sea presence, blast any concentrated force on the island and then chopper in ground forces to neutralize the rest with close air support.
The Argentines attacked because they thought Britain was too weak to respond at all and that the US would stay out of it for reasons of diplomacy. I've read the US supplied Britain with intelligence, and some of it they would have had anyway as part of NATO. My guess is the US wouldn't have let Britain outright lose as they needed the illusion of British capability to help keep the Soviets in check to some degree.
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