According to Alton Brown (of Serious Eats fame) you can safely brine a turkey for days. However, you'll need to adjust the brine depending on the duration. Yesterday I roasted a chicken that was brined for about 36 hours and the results were delicious.
AB Fan: Can I brine an 18-pound turkey overnight, or is this too long?
Alton Brown: No, it's not too long. Technically, you could brine a turkey for several days. The trick is in two things--brine concentration versus mass. You could either soak a bird for a long time in weak brine, or for a short time in a stronger one. You're better with weaker brine and a longer soak, so take the standard brine that we use in "Good Eats," and you could easily do that overnight. If you're afraid of it being too salty, you might cut back to 3/4 cup of salt instead of the full cup, but leave the sugar amount the same. I've gotten to where I really like to thaw my turkeys in brine, because I can make my brine, keep it in a cooler, toss in my frozen bird, and leave it for days if I want without worrying about the temperature getting too high. It will stay really cold, but, at the same time, the water will help thaw the bird. So when it's thawed, it's already brined. But that is an imprecise science, so you have to work with it. If I feel the brine will get too warm, I'll add a bit of ice. So far, that hasn't happened. It stays around 40 degrees.
Quoted from a forum post.