It looks like the Comfort Inn Airport / Cruise Port South
offers shuttle service to Port Everglades. Not sure about their Park and Cruise packages. I've stayed at several Comfort Inns all over the country, and they're usually pretty reasonable in terms of price, and the rooms are about average for what you pay.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)