A number of points to be addressed on this topic.
I must concur with the position that a U.S. invasion of Cuba in '61 (an important distinction compared to the next year, when the dynamics of the situation are dramatically different), being as it was squarely in the U.S. sphere of influence and not yet possessed of sufficient Soviet backing to provide a deterrent, would have yielded little in the way of response from the Soviet Union save for a significant propaganda victory.
This itself is enough, however.
One must understand that this was at a time when the U.S. was going to great lengths to promote its image as a beneficent, and importantly, non-imperialist power. Interventionism was the Soviet game, and the U.S. did not want to be seen as playing it, particularly engaged as it was in attempting to woo potential allies in the highly-sensitive third world. Eisenhower in particular cleaved to this image, as can be evidenced in his response to British and French intervention against Nasser in the Suez.
Further, Eisenhower had deep reservations about the viability of intervention as a tool for containment, citing the costly and largely inconclusive war in Korea. During the planning stages of a hypothetical invasion of Cuba, commanders expressed concern over their ultimate ability to root out guerrillas deeply enmeshed in the Cuban countryside, again citing their experiences in Korea. It was for these reasons that Eisenhower chose to adopt covert CIA operations as the primary instrument of combating global communism, seeing in it a cost-effective and (again importantly) largely deniable alternative to military intervention.
All of this was obviously predicated on the assumption that these CIA jobs were successful, which at the time it was believed they were, based upon the overthrow of Mohammad Mossadegh in Iran and the overthrow of Jacobo Arbenz in Guatamala, both of which were orchestrated by the CIA and which came to form the core of its covert operations doctrine. The last instance in particular, having been conducted in Latin America, was heavily drawn upon in the planning of the Bay of Pigs operation.
Why is this important? Because I would argue that Nixon, having been Eisenhower's Vice President, would have been more inclined to pursue the covert route in Cuba which led to the Bay of Pigs than JFK was. To really make the invasion decision a plausible one you will need an earlier PoD.
Putting that aside momentarily and postulating specifically on the substance of an American invasion of Cuba, my earlier point about military reservations yet stands. While it is certainly possible that an effective blockade could have isolated the guerrillas from supplies, the fact remains that dislodging the communists from Cuba would be a messy, messy exercise in asymmetric warfare.
Sorry if this is rambling, I'm sleep-deprived.