Unless your fridge is above 40 F (4 C), it won't go bad. I've had large frozen turkeys take 4 days to thaw before. Just use it once it is fully thawed, don't let it sit around thawed for several more days.
There's no food that I'm aware of that goes bad in the time it takes to thaw it. The stilltasty link below shows 3-5 days for refrigerated meat, and 4-6 months for frozen. Transitioning from frozen to thawed though, I generally count on defrost time + 2-3 days.
If you want to thaw it faster you can always use the cold water method. Simply place it in a sink full of cold water (submerged) and change the water every 30 minutes. The rule of thumb for turkey is 30 minutes of thaw time per pound. I imagine pork shoulder would be similar, maybe a little longer?
Additional Info:
http://stilltasty.com/fooditems/index/18060
Let's start with the assumption that Safety is never in the balance. Safety has to be taken into account for any method that we use and that means that we want to keep any food that is time and temperature sensitive out of the danger zone. The danger zone is the temperature range from 40 degrees F to 140 degrees F.
If you have plenty of time, letting the turkey defrost in the refrigerator is safest and easiest, since there is little that you have to do. The turkey is always out of the danger zone and all you have to do is put it in the refrigerator. However, it can take a very long time, 24 hours for each 5 pounds of turkey weight...4 days for a 20 pound turkey.
Assuming you haven't planned that far ahead, the other safe method is to defrost in the sink with cold running water. The water doesn't need to be pouring out, just a steady stream so the water turns over regularly. Water is a better conductor of heat than air, so the turkey will defrost more rapidly than in the refrigerator.
The danger zone is why you don't want to defrost the turkey using warm water, or just sitting on the counter. In either of those cases, the outside meat is warmed into the danger zone before the inside defrosts, so you have some of the meat (the part that is most likely to have come into contact with contaminants) in a temperature range that promotes bacterial growth.
Best Answer
It's fine to thaw for a few (or several) hours under cold water and then put it in the refrigerator. Just keep the water cold and refrigerate immediately upon removing the turkey from the water. The USDA and Butterball are being extremely overly conservative, most likely because a lot of people are really bad at following instructions. Cold water good - warm water not good
As a matter of fact, defrosting under slowly running cold water for several hours now, and refrigerating until time to cook is exactly what I would do.
I happen to live in a part of the world where I can be guilt-free about slowly running cold water for hours. There is no such thing as a water shortage here, the melting glaciers are extraordinarily huge. Thawing a turkey that way in some parts of the world (and even here in the US) would be an environmentally unsound way to do it. So in those parts of the world, be sure to buy frozen turkeys several days in advance so there is plenty of time to defrost in the refrigerator.