*Of course* the US could defeat Castro with a massive invasion (which would not have to be on nearly the scale of Normandy). That was never in doubt. But knowing of Latin American revulsion at US military intervention (a revulsion by no means confined to pro-Communists) the US wanted to make it appear that this was a "Cubans vs. Cubans" thing, just as the toppling of Arbenz in Guatemala in 1954 was portrayed as a purely Guatemalan coup.
As for what would happen if there was a massive invasion by US troops, I'll recycle an old soc.history.what-if post of mine:
***
It's very unlikely that Khrushchev would go to war as a result but it is likely that he would feel a need to do *something.* I once proposed a scenario in which his response is to do what in OTL he did a few months later anyway-- build the Berlin Wall--and I noted that then people would be speculating in this newsgroup "What if the US had never invaded Cuba? Would the Berlin Wall have been built?"
One may doubt, incidentally, that a "totally successful" invasion (in the sense of one which would actually overthrow Castro) would be a good idea from the viewpoint of *Realpolitik*, even if there is no serious reaction from Khrushchev. It would entangle the US in an extremely messy Cuban political situation: (1) The anti-Castro factions would be struggling against each other for power, and the US would have a hard time being neutral; (2) the new regime would be seen as a puppet regime even by many Cubans who were not Castroites; and (3) there would likely be guerilla warfare and terrorism by Castroites. Moreover, such an invasion would be extremely unpopular in Latin America, and anti-Yanqui feeling could grow tremendously, so that the US in destroying one Castro might create several new ones.
No doubt Clayton Fritchey, then an aide to Adlai Stevenson, had some of these things in mind when he told JFK, "Mr. President, it could have been worse." "How?," JFK asked. Fritchey replied, "It might have succeeded." (Jim Rasenberger, *The Brilliant Disaster: JFK, Castro, and America's Doomed Invasion of Cuba's Bay of Pigs,* p. 395.
http://books.google.com/books?id=0Ex08ZkkXEkC&pg=PA395 )
https://groups.google.com/d/msg/soc.history.what-if/DQFyp4RcAUQ/ErKyse2Ms3MJ