Every dentist offers different options for their patients. If you do not feel that local anesthetic is going to be enough because you are too nervous, then you should call the office and ask what additional choices you have.
Both of my root canals (done by an endodontist) were done under IV sedation and they were 100% pain free during and after. My current dentist does not offer IV, so I have had extensive work done by taking Valium before the apointment to calm me down, and nitrous during to keep me relaxed. I have to say that being a recovering dental phobic, I really like nitrous!
If you choose to have any sort of sedation other than nitrous alone, you will need someone to take you to and from the appointment. I was able to return to work the next day after all of my appointments, but was too groggy the day of to even consider it.
Honestly, the worst part of it all is having your mouth open for so long! If you are worried, then ask for a referal to an endodontist for the root canals. They often offer more options then general dentists and usually do the root canals in one appointment.
PS~ My geography stinks so I don't know if this will help, but check and see if you are near Dr. Michael Hardee. He is an endodontist in FL who offers IV sedation as well as other options.