I'm as guilty as the next gal of spouting this commonly held myth. In essence, the belief is that daughters will deliver babies similar to the way their mothers did before them. In other words, there is genetic influence over whether or not a woman delivers early, late or on time, how large the baby's weight will be and how long labor can be expected to last. Although I did seem to follow my mom's storied path, I know plenty of other women who didn't, and there's no solid scientific evidence to support generational similarities.
In fact, a child's size can be estimated based on the expectant woman's weight gain, as well as the size of both parents [source: Adams]. Also, due date prediction methods and labor processes have thankfully improved a lot over the past few decades. So, even if you and your mama did both deliver early, it's quite possible that she didn't have the correct due date in the first place!