"Before they do so" could also be translated as "Before they do this" - It's a short way of saying "Before they do the action which was just referenced" or "Before they do the activity which we are discussing", so the same words are not repeated. It would only be used immediately after the subject action being referenced - in this case, the action being "head home (for the holidays)".
As an example, it would be strange if the sentence was written this way: "Members of Congress now have only a few weeks left before they head home for the Christmas holidays. Before they head home, I urge them to do their job..." Repeating the words "head home" does not sound correct - although there isn't a problem with it grammatically; it's a choice of style. When the repeated words are desired, the writer often will emphasize them with another action word such as "do", like this: "...head home for the Christmas holidays. Before they DO head home, I urge them..."