This means that there is no longer the ability to negotiate a budget in good faith. The Dems can fight for more health care funding (or whatever) and the compromise can happen, and then the president can just say "sike!" And not do it.
And, political leanings aside, this president has shown that he will indeed break any agreement he decides to, so there doesn't seem to be any reason to negotiate. So I'm thinking this shutdown lasts a Long time.