Agree with Kevin and Phil on penetrating oil of some kind first (both of Phil's suggestions have worked well for me). For me, I've had good luck with small interior hardware like that using a small hand held 1/4" bit driver ratchet like the one below. Clean out the screw head opening to get your bit to set down as deep as possible, then using one thumb/hand to hold pressure down on the bit, twist the ratchet to break free the hardware. The torque applied with this tool has helped me break loose some really rusted/stubborn hardware.
