If you rent with National or Alamo then you'll have a free shuttle ride to/from Port Everglades. However you'll need to show them your rental contract/receipt in effect. They were strict on that.
There were a few folks (without a rental contract) that offered to pay the driver on the side but they were refused.
Budget didn't have a shuttle service. I rented with them before our cruise in Oct 2011. After the cruise it was with National.