If you're lucky and already have your Thanksgiving turkey, good for you. Be careful not to waste a bit of it, because it's going to be awhile before supplies and prices are stabilized. Buying a turkey breast early next year may not be a sensible option. There are tons of ideas on the internet to help you save and use every bit of the turkey you have.
If you don't have one yet, consider something else. Ducks and chickens are affected by the shortage, so think about having a ham or some special ethnic dish this year.
Eggs can be another problem altogether, but for frugally minded people, it's simply a matter of eating fewer. Baking for the holidays takes more eggs than usual, but you can substitute in some instances or find recipes that don't require eggs. Eggless cakes, cupcakes and bread recipes are easy to find on the internet. Many breads that call for eggs are just as good if you substitute an extra tablespoon of water and a teaspoon of baking powder for each egg.
Pumpkin pies may be a different story, but even then you can short the pie one egg without causing a problem.
Some stores have already put limits on egg purchases and turkey purchases are limited as well, but don't run out and try to get more than your share. It makes sense to be careful with the use of these two foods right now, not only because it will save you money, but because with the shortage, you will allow others to have them, too.