We're staying at the Marriott Courtyard Airport/Cruise Port in March. Don't know what you consider cheap. Check out Marriott's website to get prices, or bid on a 3 star/4 star in that area through Priceline.
Marriott does have complimentary shuttle service to Port Everglades.
Serenade of the Seas b2b January 2016
If you are active, reserve or retired military, you have the option of staying at Homestead Air Reserve Station on a Space A basis. It's about 50 miles to the port, which isn't close, but is easily doable. I stayed there last March for $33 overnight. Pretty nice room, too, Double bed, mini-fridge, microwave, coffee maker, full size tub head with seperate vanity, cable TV and DVD/VCR combo.
USS Henry L. Stimson-SSBN 655 Gold (4 Patrols 1988-1991)
USS Daniel Webster-SSBN 626 Blue (Conversion Crew)
USS Nebraska-SSBN-739 Blue (5 Patrols 1995-1998)
USS Wyoming-SSBN 742 Blue (3 Patrols 2002-2004)
Grandeur of the Seas-10/28/2005 - 10/13/2006 - 10/05/2007
Mariner of the Seas-4/2/2006
Radiance of the Seas-3/17/2007
Grandeur of the Seas-4/12/2008 - 4/19/2008- 10/30/2008
Try the Ramada Inn at the Ft. Lauderdale airport (State Route 84), which is only about 3 miles from the cruise terminals. They offer free transportation to and from the airport and cruise port, and are reasonably priced. It is a commercial motel: not a resort hotel, but should do as a place to stay the day before you sail.
Jerry, from Ft. Lauderdale area!