Public transport between Obidos and Nazare is difficult particularly on weekends when there are no buses between Obidos and Caldas da Rainha.
Trains are a difficult option as Obidos/Nazare stations are not well located close the centres.
On weekdays there is a Rodatejo bus service between Obidos and Caldas da Rainha as follows:
Obidos Caldas da Rainha
08:02 08:12 Weekdays Only
11:20 11:30 Weekdays Only
12:42 12:58 Weekdays Only
16:45 17:01 School Term Only
There are then frequent buses between Caldas and Nazare.
I have published a copy of this reply and the timetable on my blog here.
http://barlaventostravelblog.blogspot.com/2008/07/obidos-to-nazare-public-transport.html