A better design is to use a four or more space panel where the disconnect would go. Do a load calculation and feed that panel with the correct wires. Put a normal breaker in the main panel to protect those wires. Then use the 60A GFCI in the subpanel. It's also the disconnect. In the subpanel use a normal breaker to feed a GFCI receptacle.
This way when 120V loads nuisance trip the GFCI there will be less walking and the spa wont shut off.