There was considerable opposition to the the passage of the Constitution by a group commonly referred to as the anti-federalist. They primarily opposed the notion of a more powerful federal government than found under the Articles of Confederation and were particularly concerned about the ability of the Congress to levy taxes.

Like the authors of the Federalist Papers they published treatises in newspapers, with the most famous using the pseudonym 'Brutus' as opposed to the 'Publius' of Hamilton, Madison, and Jay.

Brutus captured the core issue with the following passage:

exercised without limitation [the power to tax] will introduce itself into every corner of the city and country. It will wait upon ladies at their toilet, and will not leave them in their domestic concerns; it will accompany them to the ball, the play, and the assembly.

Antifederalist also worried about the power of the government to borrow, make treaties, and create a standing army. They essentially wanted the 13 states to be able to act autonomously in the name of their own interest and only maintain a loose tie to the other states.

Bernard Bailyn discusses the Federalist Papers and their response it a chapter of To Begin the World Anew, which also has interesting chapters about a wide array of topics relating to the founding fathers. It's also short and easy to read.

The anti-Federalists, a loose political faction of people like Patrick Henry, who opposed the Constitution and the creation of the more robust federal system proposed by the Federalists like Hamilton and Madison. The anti-federalist drafted several open letters and opinion pieces that have come to be known as the "Anti-Federalist Papers."