Can a dogs broken leg heal on its own?

Take your dog to the vet! Would you just put a splint on your broken leg? I doubt it! The bone has to be set before a cast or splint is put on. Don't let your dog hobble around in pain because you don't want to spend the money at a vets. If you are truly low on funds some Animal Shelters will help out. Also, if you take your dog into a good vet you can sometimes make installments on the cost of the bill or work the bill off by cleaning cages, etc.

Edit: A splint on certain type of fractures is indeed effective. The factors to take into consideration are the age of the dog, degree and difficulty to which it has fractured, and your own dog's disposition.

If a dog is less than 6 months old, the bones heal quite rapidly. A transverse fracture can be splinted, if you run into money problems. Above all, if you ever have orthopedic procedures performed, CAGE REST your animal. They do not know to be still.