"I could (do with/murder) a cup of tea." would be a potential answer to "Is there anything I could get you?"
Both would mean "I would really like a cup of tea [i.e. I'm very thirsty]".
It's not so much polite as emphatic.
See: could - Idioms - by the Free Dictionary, Thesaurus and Encyclopedia.
- particularly "could do with" and "could murder".
PS: I notice they're not included in the UE list of idioms.
Maybe they could do with being included? But that's a polite request, rather than an emphatic one!