Welcome to callback hell! This is a little slice of callback hell =) Enjoy! I will rewrite it =)

after

function notifyServerError() {
  swal("Server failed");
};

function hidePost(id) {
  $('div[data-post-id=' + id + ']').hide("slow");
};

var update_url = '/news/update_state';

var STATE_PUBLISHED = 'P';
var STATE_DELETED = 'X';

function handlePublish(id) {
  swal(
    {
      title: 'Вы уверены?',
      type: 'warning',
      showCancelButton: true,
      cancelButtonText: 'Отмена',
      confirmButtonClass: 'btn-success',
      confirmButtonText: 'Опубликовать'
    },
    function(){
      $.post(update_url, {
        id: id,
        state: STATE_PUBLISHED
      })
        .done(hidePost.bind(this, id))
        .fail(notifyServerError);
    }
  );
};

function handleDelete(id) {
  swal(
    {
      title: 'Вы уверены?',
      type: 'warning',
      showCancelButton: true,
      cancelButtonText: 'Отмена',
      confirmButtonClass: 'btn-danger',
      confirmButtonText: 'Удалить'
    },
    function(){
      $.post(update_url, {
        id: id,
        state: STATE_DELETED
      })
        .done(hidePost.bind(this, id))
        .fail(notifyServerError);
    }
  );
};


$(function(){
  $('.btn-publish').each(function(index){
    var id = $(this).data('post-id');
    $(this).click(handlePublish.bind(this, id));
  });
  $('.btn-delete').each(function(index){
    var id = $(this).data('post-id');
    $(this).click(handleDelete.bind(this, id));
  });
});

before

$(function(){
  $('.btn-publish').each(function(index){
    var id = $(this).data('post-id');
    $(this).click(function(){
      swal(
        {
          title: 'Вы уверены?',
          type: 'warning',
          showCancelButton: true,
          cancelButtonText: 'Отмена',
          confirmButtonClass: 'btn-success',
          confirmButtonText: 'Опубликовать'
        },
        function(){
          $.post('/news/update_state', {
            id: id,
            state: 'P'
          })
            .done(function(){
              $('div[data-post-id=' + id + ']').hide("slow");
            })
            .fail(function(){
              swal("Server failed");
            });
        }
      );
    });
  });
  $('.btn-delete').each(function(index){
    var id = $(this).data('post-id');
    $(this).click(function(){
      swal(
        {
          title: 'Вы уверены?',
          type: 'warning',
          showCancelButton: true,
          cancelButtonText: 'Отмена',
          confirmButtonClass: 'btn-danger',
          confirmButtonText: 'Удалить'
        },
        function(){
          $.post('/news/update_state', {
            id: id,
            state: 'X'
          })
            .done(function(){
              $('div[data-post-id=' + id + ']').hide("slow");
            })
            .fail(function(){
              swal("Server failed");
            });
        }
      );
    });
  });
});

.bind is crucial for getting rid of callback hell =)