The current research shows that labor, particularly in first-time moms, is about one hour longer when an epidural is used. This is just an average, however, so some women will experience a longer extension of their labor, while for others it may be shorter. In some cases, the epidural can even decrease overall labor time.
Regarding paralysis, it would be incorrect to say it is impossible or never happens. However, it is so exceedingly rare that most anesthesiologists will go through their entire careers without seeing a single case of paralysis caused by an epidural. Several million women receive a safe epidural each year in the U.S. There are a few specific risk factors, most notably certain blood clotting diseases or infections, which may increase the chance of neurologic side effects but epidurals are not typically used in women who have these conditions.
William Camann is the director of obstetric anesthesia at the Brigham and Women's Hospital in Boston. He is also an associate professor of anesthesia at Harvard Medical School, and past-president of the Society for Obstetric Anesthesia and Perinatology. An internationally recognized authority on obstetric anesthesia and pain control during childbirth Dr. Camann is the co-author of Easy Labor, Every Woman's Guide to Choosing Less Pain and More Joy During Childbirth (Random House/Ballantine Books, 2006). You can find out more about his book at easylabor.net