What does it mean when someone says "that's the last thing I want/need"?

Rebecca

It means that they really don't want or need it! Out of all the possible things they could want or experience, that would be the very last thing they want. It would be the worst thing possible. Ex: Since I'm writing my exam tomorrow, the last thing I need is to be late for school. Ex: I'm so tired, the last thing I want to do is clean my house. I want to sleep!