First, anything incriminating that you do or say prior to arrest is admissible as evidence against you in court. Unlike TV, a Police Officer is not required to read the Miranda Rights at the time of arrest. They may even ask general questions not directly related to the arrest such as name, address, employer, etc. However, any questions directly related to the DUI investigation are protected by the Miranda Rights.
In June 2010 the US Supreme Court narrowed the interpretation of what constitutes invoking Miranda Rights. The Court ruled that a suspect must make a direct statement invoking their right to remain silent. Ambiguous statements, suggestions, or silence does not necessarily mean your right to remain silent has been invoked. Police may continue to question you unless you make a direct statement invoking your right to remain silent and speak to an attorney.