I used the Heimlich maneuver(be careful) on our australian shepard it dislodged it after the 5th try. If hes breathing ok I would let him deal with it for awhile, usually happens on a weekend or sunday when doc is closed. If the dog is dealing with it ok we gave him canned dog-food it seemed to move it through. Dogs are able to deal with most obstruction if they are in good health I caution putting my fingers down there throat unless I can see the obstruction first. Stay calm and think before you react.
Our boxer tried to swallow a pressed rawhide recently. He had shallow breathing that sounded like wheezing, so we massaged his neck area and tried "burping" him for a minute or two. No luck, so we got a bit of water down his throat and he started drinking some on his own. That was just enough to loosen the bone and he started to throw it up. We definitely had to help pull it out, though.
Greedy dogs do try to swallow these things before they have really chewed them small enough. One of mine once sicked up a cow hoof days after she swallowed it. It was softened somewhat but still recognisable. I never gave them again after that. You had best not give these to your dog again, now you know that he is daft enough to do this, and no, they don't learn from the experience - not when it comes to food.
I would take your dog to the vet and let them look at it
Rawhide Bones are the worst thing you can give to your dog. You could have caused the bone to scratch the inside of his throat while pushing it down, which was not a good idea. I would take your dog to the vet and let them look and see if it scratched his throat. If he vomits and there are signs of blood than most likely the bone scratched the inside of his throat. Take him to a vet just to be safe.
You should take him to your vet if its really far down in his throat because chances are you will scare him and he may bite you. Unless you can see the piece of rawhide then someone can help you keep his mouth open while you remove it, but be careful not to scare him and get bitten