I'm helping a business that handles occasions.

They have a tendency to write almost all their posts forward dated.

automatically the wordpress calendar only display as much as today

How do you overwrite it therefore it shows all of the posts, the forward dated ones?

Not regarding towards the calendar particularly, but this is exactly what I personally use to obtain future posts. You are able to alter the publish type to anything you want for those who have custom publish types registered, for example events, etc.

add_filter('the_posts', 'show_future_posts');
add_filter('pre_get_posts', 'include_future_posts');

// Show future posts when available
function show_future_posts($posts)
{
   global $wp_query, $wpdb;
   if (is_single() && $wp_query->post_count == 0)
   {
      $posts = $wpdb->get_results($wp_query->request);
   }
   return $posts;
}

// Show future posts in standard queries for afisha
function include_future_posts($query) 
{
    if ($query->query_vars['post_type'] == 'cheers' && !is_admin())
        $query->query_vars['post_status'] = 'publish,future';
    return $query;
}

The !is_admin within the include_future_posts function is needed for that admin side to operate properly with draft, released and scheduled posts. Take it off to determine what goes on otherwise.