Fairly common problem.
You can try tapping on the screw driver with a hammer as you try to turn the screw, or you can try an impact driver. I have had success with both methods, however, breaking the screw off in the housing is always a risk.
For very stubborn screws, I have also had good luck with mildly heating the housing with a propane torch. Be aware this method carries additional risks.
Before you booger up the screw, grind a bit of the tip off the Phillips screwdriver you're using. These metric cross slot screws are shallower that a standard Phillips screw. Oh, and welcome to the forum!