So, if you clam up during the imvestigation, does it mean you could be charged with obstruction?Miranda rights serve as notice that ANYTHING you say can and WILL be used against you.
They way it works is that if you are arrested, you would actually have to assert your right by communicating that you are invoking your right to be silent. If the police try to get you to talk after you expressly invoke your 5th Amendment right, it's easier to exclude those statements from evidence.
Another consideration is your 6th Amendment right to counsel. If you state that you wish to have counsel present, then the police may not ask any questions until your counsel is present. If they do, your responses may not be admissible without the prosecution showing an affirmative waiver of your rights.
Big caveat - Miranda rights only apply if you are in custody (which usually means you have been arrested). If police are on the scene and investigating or interviewing you, these rights don't come into play.
Disclaimer - this is not legal advice because I am not advising anyone specifically here on what to do in the above situation. I am only explaining how the law would operate in this type of situation.