No insurance for 01.01 – What happens?

Moin together, I have a “small” problem. I quit my car insurance company like every year and this runs out now on 31.12.2012. But now I totally failed to sit down and conclude a new insurance deal. Does anyone know how this works internally with the insurance company and the road traffic office? Would it be a problem if I only closed the new insurance on 02.01 or 03.01? My insurance representative is no longer tangible before…