Yes there are sliding scales.
Sometimes there is provision for people to work with people who are training for significantly reduced costs as well.
Some people are a little worried about the competence of therapists in training. In support of the notion I'll say that the best psychologist I've ever seen was in training. I found her to be more willing to view me as an individual than people who have been practicing for longer (with more of a 'stereotype' in effect). I also found her to be really motivated toward helping me.
It might be worth contacting universities in your area to find whether this is an option.
Another option is psychoanalytic training institutes.
The advantage of the latter is that the time it takes them to train means that you are likely to get more continuity.