Twice now I have had to keep a National car for longer than originally reserved. Both times they have been incredibly gracious, letting me have the same rate I had booked. Absolutely no problem at all.
This was once at MCO, and once during a rental where I picked up in Phoenix and dropped off in Anaheim. March for the latter, September for the former, both this year.
Yep, your contract rate is good for up to 30 days extension on your rental.