Two of the compromises in the Constitutional Convention were the Great Compromise (also called the Connecticut Compromise) and the 3/5 Compromise.
The Great Compromise settled the dispute between the states with large populations and the states with smaller populations. The small states wanted representation in the government to be equal for everyone, so that they weren't overpowered by the big states. The big states wanted representation in the government to be based on population, because they have more people, thus think that they are deserving of a bigger say in the government. Connecticut delegate Roger Sherman proposed the Great Compromise, which gave the small states what they wanted by stating that representation in the Senate would be equal across all of the states, but also gave the large states what they wanted by stating that representation in the House of Representatives would be based upon state population.
The 3/5 compromise settled the dispute over slaves and their population count in the US. The states that owned a lot of slaves wanted their slaves to count towards their total population, however, the states with less slaves did not want slaves to count towards population. This was settled as the delegates decided that each slave should count for 3/5 of a regular citizen when counting for population.
Besides geography, the major issue that would have made this impossible is that each "country" or state in South America was dominated by a different ruler, many of whom had fought of the Spanish--meaning that they would have never united under one title. Their cultures were also wildly different.
