We landed around 10:30 am last week. My husband went and got the luggage from baggage claim and I went directly and caught the shuttle to the rental facility. (It is right next to the the Hertz facility). It was about a 5-10 minute ride on the bus, and @ Thrifty site there were a lot of agents working and I only had to stand in line for about a minute. I picked up the van and was back @ the airport to pick up the husbank, kids and luggage by 11:10 am.
BTW, we had a a minivan rented using a code from Mousesavers (the Northwest code...) We had no problem using it, even though we did not fly Northwest. The agent did ask me how I got such a great rate though - she seemed pretty suprised. Then I was asked if I wanted to upgrade to a Grand Caravan for $14 more a day. She told me it had extra luggage room, built in child saftey seats etc... I had to tell her no three times! When I went out to get the van, we had a Town and County (equivalent to the Grand Caravan) for the base price.
When returning the van, be sure to leave plenty of time. I had a hard time finding the place on the way back. I dropped off the kids, luggage and husband @ the airport - they checked in using the skycap and I went to return the van... It took me almost 45 minutes. You have to use the North exit off the airport to Semoran blvd.... Good luck.