If we could all do it as perfectly and intuitively as Tracy it would probably take a week or two, but for most people it does take much longer. For us it probably took 6 weeks for her to do most naps on her own. Yes, it was a long time, but we had some success early after 2 or 3 weeks when she started having some better naps and it started taking less and less time patting to get her back to sleep at that 45 min point, so that kept us going.
I guess the longer naps didn't really *stick* though, until we got A times right, and she'll still have a short nap every now and then if her A times need tweaking again.
I agree with pp, it was worth it to me to extend those naps, get some Y time during the day, and keep her on her routine.