We may have air superiority for a day after which I strongly suspect we would be out of missiles at which point the argentine navy and airforce have free range to bring in the troops. The only hope would be that we already had an attack sub stationed in the area to discourage them but this is often not the case as we only have a limited fleet.
The war itself would take on a very different complexion as once they had taken the island they would have access to a decent run way that is long enough to operate there jets giving them imediate air superiority over the islands and we no longer have the long range bombing capability to destroy it so again we would be relying on an attack sub with cruise missiles.
The major challenge we would face would be re-taking the island, last time we pinched a significant number of merchant ships to transport our troops and supplies, we could only do this as they operated under UK flags. The UK merchant fleet is now tiny and comendering any ship flying under the flag of a different nation is deemed piracy.
We also only have two active carriers one of wich is in refit the other is in the gulf, the delay in getting a task force together and ready for sea would be huge alowing the argentines to massively reinforce the islands.
The only way we could dislodge them should they wish to take the islands would be with even more US help than last time.
Or our gov could grow some balls and tell them to move off our land or nuke the **** out of every large city they have,