It doesn't seem like version 1 of the Tumblr API supports notes. However version 2 does:
http://api.tumblr.com/v2/blog/{name}.tumblr.com/posts/text?notes_info=true
Reference
- Tumblr API v1: http://www.tumblr.com/docs/en/api/v1
- Tumblr API v2: http://www.tumblr.com/docs/en/api/v2#posts