For some reason, i'm thinking that lying to the cops, if you are under suspition that is, is not exactly obstruction of justice. To my knowlege, obstruction of Justice is when you do not turn in someone who has commited a crime, if you have knowlege of it before the police/courts do. Or, if you aid this person who commited the crime in any fashion that would "hinder or prevent his apprehension." It could also be used if you do anything to stop or delay a trial, or even just fuck with the trial, such as threatening jurors, briving them, etc. I have never heard of anything coming from someone lying to the cops while they themselves are under suspicion.
And miranda rights. They do not have to be read to you, but anything you have said to the cops before getting arrested, can not be used in court if you have not been read your miranda rights prior to the things you have said.