{"username":'myusername', "password":"mypassword"}

{"username":'myusername@gmail.com', "password":"mypassword"}

{"mail":'myusername@gmail.com', "password":"mypassword"}

["Missing required argument username"]

/**
 * Implements hook_services_resources_alter().
 */
function my_module_services_resources_alter(&$resources, &$endpoint) {
  // Override the normal user login callback.
  if (isset($resources['user']['actions']['login']['callback'])) {
    $resources['user']['actions']['login']['callback'] = 'my_module_services_login';
  }
}

/**
 * Replacement callback for the Services user login resource. Optionally use the email address to login.
 *
 * @see _user_resource_login().
 * @see https://drupal.org/node/1431724
 */
function my_module_services_login($username, $password) {
  $result = db_query(
    "SELECT name FROM {users} WHERE LOWER(mail) = LOWER(:username)",
    array(':username' => $username)
  )->fetch();
  if (!empty($result->name)) { $username = $result->name; }
  return _user_resource_login($username, $password);
}

if (valid_email_address($username)) {
$username = db_query("SELECT name FROM {users} WHERE mail = :mail",array(':mail' => $username))->fetchField();
}

{"username":"myusername","password":"mypassword"}

{"username":"mymail@gmail.com","password":"mypassword"}