An epidural will definitely remove the pain but there could be some unintended side effects. People say that without feeling the contractions, the pushing might not be effective unless the doctor/nurse give you good feedback and instructions. (I've no experience with epidurals...)
Some gynaes might be very eager to do a vacuum or forceps birth. Or they might say you need a C-section after a bit of pushing. Basically, once the gynae arrives, you have to push hard and push effectively when instructed. If you have good progress, most likely the doctor will then proceed to do the delivery promptly. From what I know, very few women push for more than half an hour without being offered a vacuum/forceps/C-sect. And most women will follow the doctor's recommendation, for the sake of our babies.