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.
Again, check out our chapter in “Patriot’s History.” Mike Allen wrote most of this, and my brief explanation here won’t do it justice. He details precisely how the term “Federalist” was originally the term for separation of powers.