Can "the least I could do" be negative? [closed]

I think it is meant to be interpreted along the lines of, "Even this thing which I have done for you is only the minimum that you deserve." It is meant as a compliment.

Another connotation is that the speaker has not gone too far out of his way, so the listener should not feel guilty about receiving something so nice: "Aw, you shouldn't have!" "Oh, it's the least I could do."

Of course I could see the phrase being interpreted in the way you are saying ironically. But generally, literal interpretation of idiomatic phases doesn't get one very far.

It means "my feelings of gratitude/condolence/sympathy/pride/etc. are much greater than this gift or act conveys alone".

It's mainly a phatic expression, but you should interpret it as a nice thing to say, especially useful when one can't think of anything more apt.

It certainly can be said with "country-club politeness", but unless it was spat out through gritted teeth and accompanied with a handshake that left you with bloody half-moon fingernail marks on your hand, you should assume they meant something nice.