Check out our extended discussion of this in "A Patriot's History of the United States."
Exactly who were these guys?
The closest I'm aware of is Hamilton, who I believe made a single not perhaps serious but indisputably maladroit reference to the need for a monarchy. I believe he was actually referring to the need for a strong single-persopn executive, not for a King.
As far as I know, his suggestion met with universal and immediate rejection.
So who were the monarchists/nationalists?
My understanding of the only two factions were the pro-Constitution Federalists (Hamilton, Washington, Adams) and the anti-Constitution anti-Federalists. The latter wanted greater state power and limited national authority.