Many times when a new client comes in to see me, a review of their paperwork shows that they made all sorts of incriminating statements to the officer during the investigation and processing phases. The explanation is usually along the lines of, "I thought I had to answer his questions," "I figured it would help if I was cooperative," or "He said he needed the information for his report."
Let's make it abundantly clear - a police officer asks questions to gain information to use against you in court! We are all familiar with the phrase "You have the right to remain silent." Let me encourage you to use it! Officer's don't engage in small talk because they think you might be someone who can turn into a close personal friend who they go fishing with on the weekends. To the contrary, the officer wants to be sure that he gains enough evidence against you to make his arrest stick and see you sent off to jail or at least penalized for the offense charged against you.
Remember that first line from your Mrianda warning - "You have the right to remain silent." Use it! While the law does not require the officer to advise you of your rights the moment you are placed under arrest, the right does in fact exist from the moment he first encounters you. In other words, as soon as the police begin an interrogation, you have the right to stop answering questions and have a lawyer advise you.
In most states, there is a minimum obligation to identify yourself and provide proof of identification, such as a driver's license. However, beyond that, you do not have to answer any questions or make any statements about the matter being investigated. My advice is to be fully cooperative with the officer in every other way. Advise him that you will not in any way resist him or try to obstruct his job duties, but politely advise that you also wish not to discuss the facts of the investigation and choose not to answer any questions. Request a lawyer and then stick to your guns. Don't let the officer play nice guy and fall for his effort to get you talking because "anything you say may be used against you in a court of law."
Very simply, you do not have any legal duty to answer questions when under investigation by a police officer, so don't. You are not going to talk yourself out of an arrest and may actually end up hurting your defense. Resist the urge to talk and, instead, let your lawyer do the talking for you.