Making up excuses in such a situation is widely seen as rude. If you tell them something like "I'm going to try to take a nap," and do not proceed to take a nap, or at least fake one, you're liable to give offense.

In a situation like this, I would very likely be taking the time to think, and telling someone that you want to think instead of talk to them is widely viewed as rude because it privileges your thoughts over their company.