While I am no fan of the flea baggers Occupy Nashville protest, I do not think they should be banned from protesting at the capitol. They should have the right to assemble if it is peaceful and not hurting anyone.
If you cant protest at the state capitol where can you protest?
Now, that is not to say that I think it is unreasonable to not allow them to set up semi permanent camps or sleep on the grounds but if they want to stand up and hold a sign all night they should be allowed to do so.
I say let them stay as long as they can stand up. Those that make peaceful protest impossible make violent protest inevitable.