I applied for a NSF post doctoral fellowship in mathematics last fall...and I got rejected.
Is it possible to obtain any feedback from NSF or from the reviewers?
I believe it's not possible. According to the program solicitation, "No written reviews are generated during the review process for this program, so the Fellow will not receive copies of reviews for proposals submitted to this program solicitation." This agrees with my understanding that no feedback is provided. There is definitely no feedback from the reviewers, and I believe the program officers also do not supply feedback.