To not spend more money than one earns or possesses; to live or operate within one's financial means. The image is of one positioning oneself as best as possible in a bed that is too small. This new job doesn't pay as well as my old one, so I'll really have to start stretching my arm no longer than my sleeve will reach. It's important to learn as early as possible not to stretch your arm any further than your sleeve, or you're going to spend a lot of your life in debt.