The obama administration and the dems were the ones who stonewalled, refused to negotiate anything, and then made the calculated decision to go ahead with the 'shutdown'.
Ted cruz cannot 'shut it down' by himself. Ultimately only the administration has the ability to do that, and it was their decision and only their decision that made it so.
Obama knew full well that he along with his media fanboys would blame the republicans for everything and the public would eat it up, which they mostly did, and they made sure to make it as big of a spectacle as they could, shutting down parks, random public spaces, barricaded open air war memorials, closed off the road with views of mount rushmore, and made sure to put signs on everything saying 'due to the government SHUTDOWN(in all caps of course lmao)'.
It was a big fucking charade