How and why did the federalists seem to overreact to the emergence of the republicans as powerful contenders for national favor? how did the republicans respond to that apparent overreaction?

The Federalists, a group made up of merchants, bankers, manufacturers, wealthy farmers, plantation owners, in other words, well-educated citizens; thought that Republicans were uneducated and a second class citizens. At Government level, those two groups were represented by Jefferson and Hamilton. Hamilton believed that elite should rule, in comparison to Jefferson who thought that a common man was capable of self-control.

Having this said, the Federalist did not want the Republicans to vote or have any voice in the new nation that was born. A few years later, both parties went to elections and in 1706 the Federalist won the elections. But in 1800, Republicans beat the Federalists and Jefferson became president of the United States. And 1812 a war took place, the Federalists vs the Republicans, and the Federalist party disappeared as a result of their defeat.