Joined: Sep 2009
Posts: 4,697
Likes: 2,039
From: Up
Bikes: Masi, Giant TCR, Eisentraut (retired), Jamis Aurora Elite, Zullo, Cannondale, 84 & 93 Stumpjumpers, Waterford, Tern D8, Bianchi, Gunner Roadie, Serotta, Serotta Duette, was gifted a Diamond Back
No you should not loosen the headset nut. That will just allow the headset to loosen and you will get a loose fork.
Normally on a quill stem, I loosen the bolt on the top of the stem about 1/2" and give it a light tap, the bolt drops back to the stem and I lift the stem up.
You may have a frozen stem that is corroded to the inside of the fork steerer. I have never had this problem so someone else could suggest a way to loosen this, I have heard of using PBblaster or vinegar.