Two senses to keep separate. (1)
搪塞 (tángsè) 'to fob off / give a perfunctory answer' — the most common compound, where
搪 means 'to fend off'. (2)
搪瓷 (tángcí) 'enamelware' — here
搪 means 'to coat with enamel'. Both come from the core idea of 'spreading a layer to block something'.