I am sure it is severely restricted. They keep a very strict reign on it and I am sure you would be sent away quickly. There may be a permitting process, but I would think it would not allow for over night. The general number is (202) 426-6841. read more
It does not appear you can camp/set up a tent in the National Mall. You can picnic in a few areas near the National Mall, but not in the Mall. You can call the rangers and ask about nearby camping. read more