Many people reacted in a good way to the new constitution, while some thought it gave too much power to the government. The Federalists supported the new constitution in 1787, while the Anti-Federalists primarily did not agree with it.
The Federalists were in support of a new constitution. They believed that the Articles of Confederation, which was the United States' first constitution, was too weak and the government needed more power. Under the Articles, the government could not tax citizens, properly create and enforce laws, regulate trade, and draft soldiers. The Federalists felt like this was weakening the country and they needed to amend it. While the Articles ended up getting scrapped altogether, the Federalists were in support of this and wanted to create a new constitution that gave more power to the federal government.
On the other hand, the Anti-Federalists favored the Articles of Confederation and did not want to amend it or create a new constitution. They associated the government having power with British tyranny and thought the power should be in the hands of the states and citizens. They opposed having a new constitution and were scared for their rights, this is why they demanded to have a Bill of Rights.