Depends on which state your in, as to how many points it is, and which insurance company you have, as to how they will grade the infraction.
But as was said above, on the back of hte ticket, there should be an option to get a court date. They will probably want you to pay a portion of the ticket, just to make sure you show up for court.
Generally, in every court I or a friend have been to (experience limited to PA and NY) you either meet with the cop or a district attorney or ADA, and they offer you some sort of lower infraction, as a compromise. The court still makes money, and you don't waste the judge's time.
I would suggest trying this. Even if you get it reduced to a 0-5mph over the limit, or a 'disobeying a traffic control device' your insurance will not be AS affected (MAY not be at all, depending on state and company).
You did well to be polite, even if the cop was a prick. That can always only help. If you do go to court, dress up, be polite, and don't use stupid excuses. Just explain you know you were in the wrong, you have no excuse but stupidity, and you were hoping that they could let you slide this once due to your otherwise clean driving record. Best of luck.