I am wanting to remove the headers above my cabinets.
Does that have anything to do with holding the cabinets up?
I want to do this to have the space above the cabinets open.
We are getting ready to resurface to cabinets and put new counter tops on.
My kitchen is stuck in the 70's.

Usually the soffit above cabinets are for appearance only. Wall cabinets are mounted to the walls, usually with screws through the back, at the top frame inside the cabinets and the frames underneath the bottom.

Make sure there is no ductwork going through the soffits.

Patty is right to give you this heads up. Plumbers use this space more than HVAC guys. I have never removed a soffit without finding a conduit arcing through the space. When the home was built that space made is easy for the elctricians to run a slow 90 degree bend through the area rather than a sharp 90. The soffit over the "kitchen desk" (bad idea) had a 3" toilet drain line running through it. BTW, as you may have guessed, theses are not called headers, headers carry the load above a door, window or ceiling.