What was said by the Anti Federalists when they were arguing on what the new government of the United States should look like?
It should also be pointed out that the anti-Federalists, some of whom included Patrick Henry and Samuel Adams, refused to ratify the 1787 Constitution unless it has a Bill of Rights attached to it. This Bill of Rights would limit the power of any future federal government that would unite the 13 states in a stronger, "more perfect Union."
The anti-Federalists were keenly aware of the abuses of government. Thomas Jefferson, who would eventually become the leader of the successor party to the anti-Federalists, to be known as the Democratic-Republicans, wrote about the abuses of supreme executive power in his Declaration of Independence. He borrowed many words and phrases from previous documents, such as the English Bill of Rights (1689) and the Virginia Declaration of Right (1776).
The Bill of Rights that we have today consists of the first ten amendments to the Constitution. The current ten originally started out as 12, but after some editing by James Madison, the First Congress narrowed the list down to 10, with ratification coming from the states in 1791, keeping their promise to list those rights retained by the people, and they also included the 9th and 10th Amendments, which reserved unenumerated powers to the people and the states respectively. This document would be used to justify the state's power to nullify federal law, though unsuccessfully. Either way, the Bill of Rights is a legacy left to "posterity" of the Framers by the anti-federalists.
The main point that the Anti Federalists were trying to make was that the national government should not have too much power. This "party" or faction felt that the state governments should have more power than the national government.
In general, this was because these people believed that the state government would be closer to the people. In other words, they believed that common people would have more of an influence over the state governments than over the national government. Therefore, they believed, the state governments would be better protectors of the people's rights.
So the Anti Federalists were concerned mainly with protecting the rights of the common people and they believed that the state governments were best at doing this.