Who or what
Felt governing power should reside with the state

Anti-Federalist.

Explanation:

Anti-federalist are those people or group of people who stand in oppose to the US Constitution. In the late eighteenth century, a group of people stood up against the ratification of the federalist government and the Constitution of 1787; they were known as anti-federalist. Though they were not very organized kind of group yet they had stronger leaders such as James Winthrop, George Mason, Patrick Henry, etc.

The anti-federalist believed that ratification of the Constitution will overpower the power of the state. They argued that the governing power should reside with the state.

So, correct answer is anti-federalist.