What is the phone number for budget truck rental? Budget Truck Customer Service Phone Number. Phone Number of Budget Truck is 1-800-475-2983, 1-800-423-1640, 1-800-952-3297. . Budget Truck is fully known as Budget Truck Rental that is a rental truck industry based in New Jersy, United States Of America.Does enterprise rent pickup trucks? One company that does rent out pick-up trucks big enough to tow travel trailers is Enterprise. On one of their web pages, they clearly state that the rental agreement must permit towing before you can use their truck to move your travel trailer.Do enterprise trucks have hitches? Enterprise Rent-A-Car locations do not allow a hitch or towing of any kind with the rental vehicle. However, towing is available on select pickup trucks at our Enterprise Truck Rental locations.