According to "This Old House" magazine, effective methods for removing a stubborn old faucet include lubricating the coupling, careful hammering and gentle heating. If these methods do not work, the remaining option is to use a faucet puller. This is a small metal hand tool that exerts tremendous pressure on the faucet without exhaustive human effort.
Stuck faucets often respond favorably to small squirts of a household lubricant. If that fails to loosen the faucet, the next option is to vibrate it gently with a towel-covered hammer. A light touch is essential because excessive force damages the sink and its faucet receptacle.
Heating is another effective strategy for loosening a stuck faucet. Portable hair dryers are excellent for this. Heat forces the metal faucet to expand and decreases friction between its moving parts. Turn the hot faucet with a wrench to prevent burns. The wrench also increases torque, making the faucet easier to turn with less effort.
According to the "San Francisco Gate," rust seriously impedes faucet removal. If this is an issue, remove surface rust with a stiff brush. If the rust is confined to the faucet exterior, brushing alone sometimes fixes the problem. However, if the interior of the faucet has rusted, it is necessary to loosen the rust by hammering.