Wordpress - How to add a data attribute to a WordPress menu item

Specifically editing the code you provided in the original question:

add_filter( 'nav_menu_link_attributes', 'wpse121123_contact_menu_atts', 10, 3 );
function wpse121123_contact_menu_atts( $atts, $item, $args )
{
  // The ID of the target menu item
  $menu_target = 123;

  // inspect $item
  if ($item->ID == $menu_target) {
    $atts['data-toggle'] = 'modal';
  }
  return $atts;
}

The second $item argument, which is being made available to your filter function, contains a menu item object. If dumped it looks something like this:

[1] => WP_Post Object
    (
        [ID] => 2220
        [post_author] => 1
        [post_date] => 2012-12-26 19:29:44
        [post_date_gmt] => 2012-12-26 17:29:44
        [post_content] => 
        [post_title] => Home
        [post_excerpt] => 
        [post_status] => publish
        [comment_status] => open
        [ping_status] => open
        [post_password] => 
        [post_name] => home-3
        [to_ping] => 
        [pinged] => 
        [post_modified] => 2013-06-05 01:55:20
        [post_modified_gmt] => 2013-06-04 22:55:20
        [post_content_filtered] => 
        [post_parent] => 0
        [guid] => http://dev.rarst.net/?p=2220
        [menu_order] => 1
        [post_type] => nav_menu_item
        [post_mime_type] => 
        [comment_count] => 0
        [filter] => raw
        [db_id] => 2220
        [menu_item_parent] => 0
        [object_id] => 2220
        [object] => custom
        [type] => custom
        [type_label] => Custom
        [title] => Home
        [url] => http://dev.rarst.net/
        [target] => 
        [attr_title] => 
        [description] => 
        [classes] => Array
            (
                [0] => 
                [1] => menu-item
                [2] => menu-item-type-custom
                [3] => menu-item-object-custom
                [4] => current-menu-item
                [5] => current_page_item
                [6] => menu-item-home
            )

        [xfn] => 
        [current] => 1
        [current_item_ancestor] => 
        [current_item_parent] => 
    )

To target specific menu item you need to formulate your condition and check it against data available in the object, for example if ( 2220 == $item['ID'] )