Since an old Mad About You episode about the "window" of opportunity to get an epidural being closed for Jaime, women have been very nervous that they too will find that there is a window they've missed if they wait too long. Good news - that's generally a myth.
Most hospitals and anesthesiologists want you to be as comfortable as possible. And let's face it, they make money when you have an epidural. So... it's in their best interests to keep you comfortable and happy.
While it may be more difficult to hold still during the administration of an epidural in very late labor, say after eight or nine centimeters. This is because the contractions are coming close together. Using your doula or your nurse, usually husbands are required to leave in most hospitals for the administration of the epidural, to help you remain calm and focused, you should have no problems.
If an epidural is delayed until you are pushing, it may be harder to use an upright position for the placement of the epidural. If this is the case, you may need to lay on your side to get the epidural. This is because your baby is likely to be further down into the birth canal making it harder to sit up.
So the bottom line is that you shouldn't be refused an epidural unless your baby's head is crowning (coming out) or you have a medical reason why you can't have an epidural.
There is the possibility that the medication will not take effect prior to your baby being born, but there is no way to accurately gauge that without a crystal ball. If you are really in need of immediate relief you can use IV pain medications instead of or until you can get the epidural. Delaying an epidural may also reduce some of the risks associated with this procedure.