I think nativity scenes should be allowed on public property. Although I do not believe that crosses, menorahs or other blatantly religious objects should typically be allowed on public property, I see nothing wrong with a nativity scene. It is just a scene of a birth. This is not overtly religious and should be allowed.
The idea of the separation of Church and state has been taken to its illogical extreme. The Founders wanted to prevent the states from banning religions, not necessarily preventing the states from promoting religion. Also, the concept of "public property" has been bastardized. Now public property is interpreted as property held in the exclusive control of a government agency (sometimes) trust for the people. Originally, public property was really the Commons, developed or controlled land that was open to all.
This violates the constitution. I am not even American, but I can tell you that this is a waste of tax dollars. If your government shut down, they should be more worried about getting back on its feet. If we have nativity scenes on public property, we should have an atheist one or a Muslim or Hindu one as soon as the Christian one. And let's not forget that Shrek and the Flying Spaghetti Monster want their monuments as well.