Perhaps, perhaps not. Keep in mind I think she should resign so this is something of a devil's advocate position.
Your position is that if she refuses to follow the duties that she is sworn to do, she should resign. Obama openly stated that he will not enforce all the laws of the land, as he is sworn to do (illegal immigration not being enforced on non-felony illegals), should he resign? Presidents have historically chosen to not enforce certain laws and they were never forced to resign over it, why is she different?