I accidentally booked for 31 days on a 30 day visa. What are my options?

I was careless in my booking times for my flight. I made sure that I had not booked more than 30 days by flying in on the 28th of dec and flying back on the 27TH of Jan. I figured that would be more than fine. But I did not think of the extra day in January. It has 31 days and I made a mistake.

Can I extend my visa? Flights would be horribly expensive to change one months out. Is staying the extra day really too bad? I'll even camp in the airport if needed.

What can I do to help myself here?