Thrifty - What has been your experience if one arrives the next day?

I have a 3 day reservation I made months ago. I will be renting over the Christmas holidays. At the time I made the reservation, the rates were very good. If I am delayed until the next morning, will they make me pay the current super high rates or would they let me keep what I have. If I have to pay current rates, the rate would more than triple.

I should have booked a backup reservation arriving the next day but I did not do so.

What has been your experience when one arrives the next morning? Will they keep the original rate or will they rebook at the much higher rate?