How forgiving is a judge about a fine that is 1 day late?

I was arrested for a PI. I went to court and the prosecutor gave me the option to pay a $200 fine within 60 days of the day I was in there along with no other charges until December or tickets. I mistook the 60 days as 2 months from May 31. So I went to the court ready to pay the fine on July 31. But the clerk said the fine was actually due on the 30th so I was a day late. No I have to attend a hearing on Dec 13 before a judge on why the stipulations were not followed. How forgiving will a judge be on this? I have no criminal background (don't know if that matters) and it was an honest mistake on my part. I got my paper stamped by the clerk showing I was there willing to pay the fine. It wasn't that I had no intention on paying it. I want this charge dismissed. But I have no idea how judges work and have never appeared before one. Any advice? It is Dallas County by the way.