Here is another vote to reserve a larger car... I have travelled with kids and with all their assorted stuff and it bulks up pretty fast. Especially with 2 car seats, strollers and Pack and Plays!)
A year or so ago, we reserved a full size car with National and ended up with a Buick Century. I will tell you that after everything was STUFFED into the trunk, I had to load up the front seat as well. (There were only 3 of us then) We did have a lot of luggage as my son was smaller then, large stroller, etc., and we were also on a 2 week trip so we had extra stuff. That Century was full to roof on our trip from Ft Lauderdale to Orlando 1/2 way through our 2 weeks.
If you do get to Orlando, and they do no give you a free upgrade and you are end up with the Neon, and you find out you can't fit it all in the car you will have 2 choices then..... You will have to make two trips which is very painfully with small kids, or you will have to request an upgrade and at that point you are at the mercy of the rental agent and the going rates.. Better safe than sorry is my motto.